Generally, this method works great for a variety of applications such as calculating employee time cards, trip travel time, flight segment times, pilot logbooks, and other transportation logbook entries to name a few.

Entering time in the correct format or expression

Look at the following expression for time:

Example:             5:26

Where: “5” represents the number of hours and “26” represents the number of minutes.  The hours and minutes are separated by a colon “:”.  In the calculator method of Captain Dave’s Time Add the colon is replaced by two separator zeros -“00”.

Look at the diagram on page one and notice the middle symbols:      “:” and “00”

This representation can help you visually remember that the colon and two zeroes are interchangeable.  Use a colon when writing the expressions on paper and two zeroes when entering the expressions into a calculator.

To use Captain Dave’s Time Add replace the colon with two zeros and the expression changes from:

Example:   5:26      is represented by    50026

When entering just hours separators must continue to be entered as well as minutes:

Examples:           2 o’clock is represented as 20000.

3 hours is represented as 30000.

1500 military time is represented as 150000.

Next, minutes are entered as the last two digits:

Examples:            34 minutes is represented as 34.

Combined with hours the entries become:

Examples:            9:34 am is represented as 90034.

16:40 military time is represented as 160040.

Minutes are always entered as two digits (although most calculators will ignore the first 0 if the time added is less than 10 minutes.

9:02 is represented as 90002.

:07 minutes is represented as 07 or just 7.

So, you the inquisitive student asks, “What are the middle two zeroes for?”

They are “separator digits” which as you might suspect separate hours from minutes.  I used two zeros because it works and there are two dots in the colon that is normally used to separate the hours and minutes.

Note:  This expression can also work for 5 minutes and 26 seconds.  Captain Dave’s Time Add works equally well adding minutes and seconds as it does for adding hours and minutes.

MEMORY JOGGER – TWO zeroes replace the TWO dots of a colon.

If you are working with AM numbers and PM numbers, the PM numbers should be converted to Military time by adding twelve hours to the PM time expression.  This can be done either before entering in the calculator or by adding 12 hours to the entry in the calculator:

Example:  4:15 PM converts to 40015 + 120000 = 160015 military time in the Captain Dave’s time Add format.

Now let’s try a simple time add example:

3 hours and 12 minutes plus 2 hours and 16 minutes is entered as:

30012 + 20016 = 50028 which is 5:28 or 5 hours and 28 minutes.

With just a little practice you can see that it is easy to read the numbers correctly in the new format, recognizing that the two zeroes in the third and fourth columns represent the colon.

But wait! There’s more…

THE MAGIC NUMBER 9940!

The magic number is an algorithmic number used to fix time expressions that do not fit the normal representation of time.  You probably remember that if you add zero to any integer the value doesn’t change.  Also, if you add the number one and subtract the number one then you’ve really added nothing at all.  Expressed mathematically:

Examples:           8 + 0 = 8

+1 – 1 = 0

Therefore,          8 + 1 – 1 =  8.

We also know that one hour equals 60 minutes.  So if we add one hour and subtract 60 minutes we really haven’t added or subtracted anything other than zero!  Written in Captain Dave’s time add format:

Example:  10000 –  60 = 9940.  1 hour minus sixty minute equals zero

Therefore 9940 in Captain Dave’s Time Add format equals zero!

Memory Jogger – the Magic number 9940 is one hour minus 60 minutes

WHEN TO ADD  (or subtract) THE MAGIC NUMBER

The Magic number is used to convert expressions with more than 59 minutes in the minute’s columns to hours and minutes by adding zero to the expression.

“When the last three digits are greater than 59, add the magic number!  9940"

ADD  9940      IF the last three digits > 0059

On page one look at the left hand side of the diagram.  This side of the diagram reminds you what to do when the minutes are greater than 59:

Now, take a look at the following addition:

Example: Add 3 hours and 49 minutes to 6 hours and 35 minutes.

30049 + 60035 = 90084 or nine hours and eighty four minutes

Focus in on the last three columns of the expression  90084.  I’ve enlarged and boldfaced the digits to consider.  The ADD THE MAGIC number rule states: “When the last three digits are greater than 59, add the magic number!”  Since 84 is greater than 59 add the magic number to the answer.  Restating our previous example:

Example: Add 3 hours and 49 minutes to 6 hours and 35 minutes.

30049 + 60035 = 90084 or nine hours and eighty four minutes

Then adding the magic number 9940 results in:

30049 + 60035 = 90084

90084 + 9940 = 100024!

The magic number has magically converted the extra minutes to an extra hour and the correct number of minutes.    The answer is 10 hours 24 minutes.

Try this example:

Examples:  90050 + 12= 90062 + 9940 = 100002 or ten hours and two minutes.

Now, suppose you want to add several number expressions of time together such as in a logbook:

Example:             4:30 + 4:32 +5:50 becomes;

40030 + 40032 + 50059 = 130112

But,   the last three digits are larger than 59 so;   130112 +9940 = 140061

But the last three digits are still larger than 59 so;

140061 + 9940 = 150001 or 15 hours one minute.

NOTE:  I just kept adding the magic number until the last three digits were less than 60.  If you are adding an extensive list of numbers it is often easier to add the magic number every so often so as not to get confused.  The Magic number can be stored in the memory of many calculators for easy repetitive entry.  Suppose I want to add the following 5 numbers together: 23 minutes plus 35 minutes plus 1hour 42 minutes plus 2hours 48 minutes plus 58 minutes.

Example:                0:23    becomes>>>         23

+0:35                                   +35        = 58

+1:42                                   +10042                 = 10100

+2:48                                   +20048 = 30148

0:58                                     +58        =30206  (I think I’ll add the magic number)

+0                                         +9940    =40146 (better do it again)

+0                                         +9940    =50086 (better do it again, the last three digits are > 59)

+0                                         +9940    =60026 (There, I recognize that number)

= 6:26 (six hours twenty six minutes)

Saying out loud the caIculator entries, “23 minutes plus 35 minutes plus 10035 plus 20048 plus 58 minutes results in the expression 30206 where the last three digits are greater than 59, so I’ll add 9940 which results in the expression 40146, but the last three digits are still greater than 59 so, I’ll add the magic number 9940 which results in the expression 50086.  The last three digits are  still greater than 59 so, I need to add the magic number 9940 again and the result is 60026.  Since the last three digits are less than 60 I must have the correct answer, 6hours 26 minutes.”

If your column of numbers continues, then just continue adding the numbers in the correct format and keep adding in the magic number occasionally to get a number that looks familiar.

If you get so excited adding in the magic number that you add it in a few too many times, then your answer might look like this:

From our previous example:                       +9940    =40146 (better do it again)

+0                                         +9940    =50086 (better do it again, the last three digits are > 59)

+0                                         +9940    =60026 (better do it again, this is fun!)

+0                                         +9940    =69966 (Once more. Whoopee!….)

+0                                         +9940    =79906 (Stop me!….@\$#% oops!)

Now, what do you do?  Well, first take a look at the two zeros in the middle that normally represent the colon.  Do they look like numbers in the upper 90’s?  YES! If so, then subtract the magic number until the answer makes sense “so the middle digits are zeros again and the last two digits are less than 60.”

If the expression kind of looks like “_ _ 99 _ _”  then subtract  the magic number 9940.

This algorithm or action is represented by the right hand side of the diagram on page one.

You can learn that you can put the magic number in the memory of many calculators and quickly add or subtract it without too much care.

Continuing our previous example:

79906

-0                                         -9940     =69966 (better do it again….)

-0                                         -9940     =60026 (better do it again…There that makes sense!)

So, you’ve learned one instance to subtract the magic number here’s another one.

SUBTRACTING TIME

Suppose you want to calculate how much you were at work today.  You showed up to work at 8:37 AM and got off work at 5:08 PM.  How long were you at work?

+5:08 PM  becomes>>    50008 + 120000 = 170008 to convert to military time

-8:37 AM                            -80037                 = 89971 (There’s those pesky upper 90’s again)

-0                                         -9940                    = 80031(subtract the magic number to get rid of the 99)

8:31       I was at work 8 hours and 31 minutes today.

Subtraction is just like adding negative numbers!

CAVEATS

• Suppose you’ve added a few times together or subtracted a few times and you get an answer where the middle two digits are way off…

Example:             543533   Well, you’ve probably made a data entry error and you need to start over.  Next time run the magic number algorithm more frequently and write down your answers as you go if you need to.

• Another common error is forgetting to convert to military time before subtracting.  Solution – start over and convert all times to military time by adding 120000 to convert PM to Military.

• Going past midnight requires special care.  Suppose you went to work at 8:04 PM and got off work at 3:37 AM.   The short answer is mentally add and/or subtract 12 hours from both entries  before entry which swaps AM to PM and vice-versa:

Example: 150037-80004 = 70034 or 7 hours and 34 minutes at work.

I subtracted 12 hours from each number causing 8:04 PM to become 8:04 AM and I subtracted 12 hours from 3:37 AM making it into 3:37 PM or 15:37 military time.

This works because 12 hours +12 hours minus one day equals zero…again we are adding zero.  Adding 12 hours and subtracting 12 hours also equals zero.

• Just as you learned in school, when the answer you seek is a negative number you’ll have to swap the numbers around and place a negative sign in front of the answer:

Example: 5:01-6:45 =  -(60045-50001) = - 10044  or -1:44  “a negative 1hour 44 minutes.”

• Thompsons Time add also works for minutes and seconds since 60 seconds equal a minute on the same “number base 60” as minutes and hours are also related on “number base 60”.

History of Captain Dave’s Time Add for Calculators

For approximately 10 years I worked for commuter airlines where time sheets were written down and manually submitted for payroll and on time performance monitoring.  I remembered doing something called integer programming in college for manipulation of very large and very small numbers.  This is similar to calculations using a logarithmic scale.  The tedious adding and subtracting of time by me and fellow pilots; doing the mental gymnastics to add and subtract time in one’s head, which was already a asea in performance calculations, weight and balance calculations, limitation numbers, regulation numbers, and various interpolations proved to be quite error prone.  So, I devised this method and taught it to many a new copilot.

Captain Dave’s Time Add has also been devised for mental manipulation of time expressions.  See the article associated to this one “Captain Dave’s Time Add – Mental Method” to learn how to do similar calculations in your head quickly, painlessly, and easily.

Captain Dave’s Time Add is a variation of mathematical algorithms known as integer programming. These families of algorithms are also used in logarithmic expressions and scientific notation of large numbers.

Captain Dave is, as of 2017, a pilot for a major airline.  He uses his Thompson Time Add methods frequently at work, in calculating flight segment times and estimated times of arrival.  On a typical transoceanic flight there may be as many as 40-50 calculations per flight to get the estimated time of arrival over various fixes or checkpoints along the route.  These calculations are done in cruising flight after the actual time of departure has been entered on the flight plan to monitor fuel burn, optimum wind economy, and forecasted winds aloft.

Captain Dave began flying at the age of 15 in southwest Kansas.  He completed his preliminary flight training and worked as a commercial pilot and flight instructor in college.

Captain Dave graduated from Wichita State University in Wichita, Kansas, USA in with a Bachelor of Science in Aeronautical Engineering. He worked for Beechcraft aerospace for three years as an engineer before returning to a career as a professional pilot.

If you’ve already read and learned the Captain Dave’s Time Add Method for Calculators you will find that this Mental Method has little or nothing to do with the Calculator Method.  It is very different, hence a different article needed to be written to explain it.   You may also find the subtraction method a little confusing at first, but stay with it. There are two methods for subtraction.  Either works just fine, but sometimes using the alternate method is a little easier to understand and use.  With some practice you can learn which method of subtraction is easiest for you in each situation and intuitively pick the easier one. Good luck, enjoy your studies, and have a happy time computing time!

A Little Background Checkup

Most likely when you were in elementary education you learned to count.  You probably learned even numbers and odd numbers.  Then you practiced counting by twos, “Two, four, six, eight, ten, twelve” and “one, three, five, seven, nine, eleven.” If so, then you are ready to learn this method of adding and subtracting time mentally.  If not, simply memorize the number sequences above.

MEMORY JOGGER – Sing this jingle to learn your even numbers, “Two, four, six, eight, who do we appreciate?  Six, eight, ten, twelve is when we delve.”  To memorize your odd numbers, sing, “One, three, five bees in the hive.  Five, seven, nine, eleven, bees go to heaven.”  Okay, so it’s a little silly.

Also, let’s review basic mental addition for base 10 numbers (the numbers you already use everyday).  Start adding the singles column of numbers, then the tens, then the hundreds and so on.

Example of Basic mental addition of numbers:

+697

Add the singles column first:  3 + 7 = 10    but, you write the 1 above the tens and the 0 below the 7 in the singles column:                             1

543

+697

0

Then you add the tens column:   1 + 4 + 9 = 14 but, you write the 1 above the hundreds column and the 4 below the tens column:               11

543

+697

40

Finally you add the hundreds column:   1 + 5 + 6 = 12 and this time you write the 12 below the hundreds column:                                                           11

543

+697

1240

So, your answer is 543 + 697 = 1240. Remember?  I hope this is all the review you need to remember how to properly add large numbers.  To mentally add time using the Thompson Time Add Mental Method you are going to combine basic addition and counting by twos.

First let’s add a couple minutes together:   3 minutes + 7 minutes = 10 minutes

Next let’s add larger groups of minutes together:  24 minutes + 22 minutes = 46 minutes

Note that, so far, the addition has been straight forward if the total minutes added are less than one hour (or 60 minutes).  But look what happens when we add sums of minutes that exceed one hour (60 minutes):

Example:   47 Minutes + 23 Minutes equals 70 minutes (which is greater than one hour or 60 minutes)

We could subtract 60 from the answer and add one hour (just like in the Captain Dave’s Time ADD Calculator Method), but there is an easier way to do this.  First, let’s write our expression using a colon to separate minutes from hours and if the hours = zero, and then let’s write down the zero and the colon to make this easier to understand.

Example:  write 0:24 to represent 24 minutes and 0:22 to represent 22 minutes

Our example then looks like a time expression:                                0:24

+0:22

0:70

BUT, 70 is not a correct expression for minutes in the hours and minutes format!  To correct this expression simply…

COUNT UP BY TWO TWICE anytime the tens of minutes column sum is greater than 5

In our example 7 is greater than 5 so we count up from seven by two, twice…

Our corrected example then looks like a time expression:                                              0:54

+0:22

1:16

A more correct way of saying it would be “anytime the tens column crosses between the digits 5 and 6, then count up by two, twice.”

“Counting up by two twice” is an algorithm.

MEMORY JOGGER – The column of colons just comes right on down the page.  The column of numbers just to the right of the column is where the “count up by two twice” algorithm is used.  I can used the column of colons to show me where to use the “count up by two twice” algorithm.

Here is another example:                                                    0:59

+0:59

1:58

Saying the process out loud, “In the single minutes column 9 plus 9 equals 18, carry the one write down the 8.  In the tens column 1 plus 5 equals 6, 8, 10 (count up by two twice since it crossed the 5-6 boundary).  10 plus 5 equals 15 write down 15.  The answer is one hour and 58 minutes.”

Let’s suppose we have some hours mixed in.

Here is an example:                                                            4:49

+2:13

7:02

Saying the process out loud, “9 plus 3 equals 12, carry the 1 and write down the 2. In the tens of minutes column, the carried one plus 4 equals five, plus one equals 6, which is greater than the 5-6 trigger.  So 6,8,10*.  Carry the one and write down the zero.  In the hours column the carried one plus 4 equals five, plus 2 equals 7.  Write down the 7. The answer is 7 hours and 2 minutes.”

Here is another example:                                                    4:41

+2:53

7:34

Saying the process out loud, “1 plus 3 equals four. Write down the 4.  In the tens of minutes column, 4 + 5 = 9 which crosses the 5-6 trigger, so 9, 11, 13*.  Carry the one and write down the three.  In the hours column the carried 1 plus 4 equals 5 plus 2 equals 7.  Write down the 7.  The answer is 7 hours 34 minutes.”

Why the 5-6 trigger?

Well, anytime you have a tens column number greater than 5 then the answer must be 60 minutes or more.  Therefore, counting up by two twice adds one hour and subtracts 60 minutes.  The reason I state the 5-6 trigger is to distinguish it from answers that have digits less than 6 in the tens of minute’s column.  Note that if we add 50 minutes to 50 minutes the tens column initially reads zero which is less than 6.  But, since the answer was actually 10 in the tens column, which is really greater than 5 the algorithm must be used.  The algorithm converts 100 minutes to 1 hour and 40 minutes (Say “ the zero plus zero equals zero in the units column, then 5 plus 5 equals 10, 12, 14. So I write down 140 or one hour and 40 minutes”).  You just counted up by two twice, instead of doing the mental gymnastics of subtracting 60 minutes and adding one hour.  The algorithm just does the math for you in an easier manner.

So, suppose you have 4 or 5 units of time to add and your calculator got left at home in the sink full of water….and then in the trash.  Think about the 5-6 boundary and count up by two every time it gets crossed, whether that’s at 5-6, 15-16, 25-26, and so on:

Example:                                 0:56

0:40

2:31

1:50

+0:32

?????

Saying the process out loud, “In the single minutes column 6 plus 0 equals 6, plus 1 equals 7, plus 0 equals 7, plus 2 equals 9. Write down the 9. In the tens of minutes column 5 plus 4 equals 9, 11, 13* plus 3 equals 16, 18, 20*. 20 plus 5 equals 25, plus 3 =28, 30, 32*. Carry the 3, Write down the 2. In the hours column the carried 3 plus 0 plus 0 = 3, plus 2 equals 5, plus 1 equals 6 plus 0 equals 6.  Write down the 6.  The answer therefore must be 6 hours, 29 minutes. 6:29.” Note that the algorithm was used three times in the tens of minutes column:

1. Crossing 5-6

2. Crossing 15-16

3. Crossing 25-26.

I didn’t have to add or subtract to use the algorithm, I just counted up by two twice.

Subtracting time is similar in nature to adding, but the boundary is changed.  Make sure you understand and can accurately add time using the mental method before learning how to subtract time mentally.

Remember when you learned to subtract numbers.  You would first look at the digits in the singles column then “steal” ten from the tens column if the number on the bottom of the equation was larger than the number on the top of the equation.

Example:                               45

-37

??

Saying the process out loud, “Looking at the single column, since the 7 is greater than the 5, I’ll steal a 10 from the next column to the left and add it to the 5. This leaves a 3 in the tens column and 15 in the singles column. In the singles column 15 minus 7 equals 8. Write 8 under the singles column. In the tens column I had a 4, but it is now a three.  Three minus 3 equals 0, so I’ll leave a blank in the tens column since I am finished.  The answer to 45 minus 37 equals 8.”

This process would repeat similarly for three and four digit numbers. It would repeat for as many digits as I had in the equation.

Now, let’s look at how this concept works for time subtraction.  Just as we “stole” a ten from the tens column if the lower digit of the singles column was greater than the upper number in the singles column…

“If the lower number(subtrahend) in the tens of minutes column is greater than the upper number(minuend) in the tens of minutes column then ‘steal’ one hour from the hours column and add 60 minutes to the minutes by counting up by two, thrice from the upper number in the tens of minutes column.*”

Wow, that’s a mouthful! Luckily, it’s easier to do than it is to say – not quite, but almost entirely unlike the way juggling is easier to say than it is to do.

Let’s do an example and you’ll see that it is easier than it sounds:

Example:   I went to work at 8:40 and left work at 16:22 military time.  How long was I at work?

16:22

-   8:40

??:??

Saying the process out loud, “Starting in the single minute’s column, 2 minus 0 equals 2. Write two below the single column.  Looking at the tens of minute’s column, since 4 is greater than 2, I need to count up from the two by two thrice -   2, 4, 6, 8*. 8 minus 4 equal 4.  Write 4 under the tens of minute’s column. In the hour’s column, I stole an hour, so the six becomes a 5.  Since 8 is greater than 5 I need to steal a one from the next column to the left, leaving a zero in the tens of hours column and a 15 at the top of the hours column. 15 minus 8 equal 7. Write 7 under the hour’s column.  Therefore, I was at work 7 hours and 42 minutes.”

MEMORY JOGGER – An easy way to keep track of counting up by two thrice is to count on your fingers.  I touch my pinky finger to my thumb as the starting number then each time I count up by two I touch the adjacent next finger. When my thumb and index finger touch, I am done counting. That makes the OKAY hand sign.  Now would be a good time for you to practice counting up by two thrice.

Note that for subtraction the count is done three times where as in addition the count algorithm is only two times.  Also, note that in addition you paid attention to the 5-6 boundary, but in subtraction you paid attention to the zero boundary (the upper number is smaller than the lower in the tens of minutes column).

MEMORY JOGGER POEM –

“When I added time and the tens

Of minutes exceeded five,

I counted up by two

Twice to stay alive.

But, when I subtract

And lower tens are larger,

I sign OKAY and just count up

By two a little longer.”

Let’s do a few more examples:

2:34

-:56

Saying it out loud, “In the single’s column, since 6 is greater than 4 I’ll steal 10 from the next column to the left and add it to the 4. 14 minus 6 equal 8.  Write down 8 under the single column. In the ten’s column, since I stole ten the 3 becomes a 2.  Since 2 is less than 5 I’ll steal an hour from the hours column and put 60 minutes in the minutes by counting up from the 2, by two, thrice. 2, 4, 6, 8*. Eight minus 5 equals 3. Write 3 below the tens of minutes column. Since I stole an hour the hours are now one.  Write one below the hours column.  The answer is One hour and 38 minutes. 1:38.”

Here’s another example:

15:46

-14:53

Say it out loud, “In the single’s column 6 minus 3 equal 3. Write 3 under the single’s minute’s column.  In the tens of minutes column; since 5 is greater than 4, I’ll steal an hour and add the minutes 4, 6, 8, 10*.  10 minus 5 equal 5. I’ll write that under the tens of minute’s column. In the hours, 14 minus 14 equals 0.  The answer therefore must be 0 hours and 53 minutes. 0:53”

Here’s another example:

15:06

-14:53

Say it out loud, “In the single’s column 6 minus 3 equal 3. Write 3 under the single’s minute’s column.  In the tens of minutes column; since 5 is greater than 0, I’ll steal an hour and add the minutes 0, 2, 4, 6*. 6 minus 5 equal 1.  . I’ll write that under the tens of minute’s column. In the hours, 14 minus 14 equal 0.  The answer therefore must be 0 hours and 13 minutes. 0:13.”

One more example:

15:01

-14:53

Say it out loud, “In the single’s column 1minus 3 equal OOPS!  3 is greater than one so, I have to steal 10 minutes from the next column.  I could steal it from the 0 and then steal an hour from the 15 hours, but that is too complicated and too easy to get lost, so instead, I’ll steal the ten minutes from the 5 by adding a small one in the tens of minutes column; making it a 0 minus 5 minus 1. I then have 11 in the single minute’s column minus 3 which is 8.  Write 8 under the single minute’s column.  Now in the tens of minute’s column I have 0 minus 5 minus 1. Since 5 is still greater than 0, I’ll steal an hour’s worth of minutes from the hours column... 0, 2, 4, 6*.  6 minus 5 minus 1 more equal 0.  I’ll write that under the tens of minute’s column. In the hours, 14 minus 14 equal 0.  The answer therefore must be 0 hours and 8 minutes. 0:08.”

NOTE: it is actually easy to account for the stolen 10 minutes by simply doing the usual math then counting backwards by one from the answer in the tens of minute’s column. Or, just for jollies, you can also add the borrowed 10 to the bottom number, making the 5 a 6 – then when you try to subtract 0-6 in the tens of minutes column and count up by 2 thrice the math becomes “0,2,6 minus 6 equals 0 in the tens of minutes column.”  This works because adding to the operand is like subtracting from the numerand.

Here is yet another example of this process in action:

15:01

- :02

Say it out loud, “In the single’s column 2 is greater than one so, I have to steal 10 minutes from the next column.  I could steal it from the 0 and then steal an hour from the 15 hours, but that is too complicated and too easy to get lost, so instead, I’ll steal the ten minutes from the next column by adding a small one in the tens of minutes column; making it a 0 minus 1. I then have 11 in the single minute’s column minus 2 which is 9.  Write 9 under the single minute’s column.  Now in the tens of minute’s column I have 0 minus 1. Since 1 is still greater than 0, I’ll steal an hour’s worth of minutes from the hours column – 0, 2, 4, 6*.  6 minus 1 equal 5.  I’ll write that under the tens of minute’s column. In the hours, 15 minus the one I stole equal 14 hours.  The answer therefore must be 14 hours and 59 minutes. 14:59.”

Hopefully, you are not too confused by this point.

SUBTRACTING TIME ALTERNATE METHOD

Remember when you learned to add time, you counted up by two twice? Well, it also works to shift into reverse and ease out on the clutch when subtracting.  Instead of counting up by two thrice when subtracting, you can alternatively count down by two twice!  Notice that if you are counting in base 10 by twos the singles digits repeat again and again:

Example:  2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40… and 1 3 5 7 9 11 13 15 17 19 21….

Look what happens if I pick a number in the middle of the series, say 18 and count up by two thrice 18, 20, 22, 24*. The singles column is a 4.  Conversely, is I count backwards from 18 by two twice 18, 16, 14* I also get a 4 in the single’s column.   The only difference that the tens column has a different value.  If this were tens of minutes instead of base ten counting, then the hour would be different…but, not really.  You see if you are subtracting and you need to steal an hour then the value of the hours column is one less. In this case ignore the 1 or 2 in this example and just focus on the 4 you got from the algorithm and reduce the hour’s column by one.  The answer will be the same.  It is just usually easier to count upwards by two thrice than to count backwards by two twice.  Let’s retry some examples using this alternate method.

Example:   I went to work at 8:40 and left work at 16:22 military time.  How long was I at work?

16:22

-   8:40

??:??

Saying the process out loud, “Starting in the single minute’s column, 2 minus 0 equals 2. Write two under the single’s column.  Since the 4 is greater than the 2 I need to steal an hour and convert it to 60 minutes.  Counting backwards the ten’s of minutes column becomes 2, 0, 8* (or 12, 10, 8) because I am going to I know the digits will continually cycle as long as I count by twos. Therefore, in the tens of minute’s column I have 8 minus 4 equal 4. Since I stole an hour the hours become 16 minus 8 which is 8 then count backwards one to account for the stolen hour. So, saying the hours again, ’16 minus 8 minus 1 equal 7.  I write 7 under the hour’s column.  The answer is 7 hours, 42 minutes.”

Next example:

2:34

-:56

Saying it out loud, “In the single’s column, since 6 is greater than 4 I’ll steal 10 from the next column to the left and add it to the 4. 14 minus 6 equal 8.  Write down 8 under the single column. In the ten’s column, since I stole ten the 3 becomes a 2.  Since 2 is less than 5 I’ll steal an hour from the hours column and put 60 minutes in the minutes by counting down from the 2, by two, twice – ignoring any extra columns of digits for now  2, 0, 8*.  Eight minus 5 equals 3. Write 3 below the tens of minute’s column. Since I stole an hour the hours are now one.  Write one below the hour’s column.  The answer is One hour and 38 minutes. 1:38.”

Here’s the next example using the alternate subtraction method:

15:46

-14:53

Say it out loud, “In the single’s column 6 minus 3 equal 3. Write 3 under the single’s minute’s column.  In the tens of minutes column; since 5 is greater than 4, I’ll steal an hour and subtract the ten’s of minute’s column 4, 2, 0, *.  Since 5 is still greater than 0, I must’ve meant to use a ten instead of a zero. 10 minus 5 equal 5. I’ll write that under the tens of minute’s column.   I could have randomly picked any starting point large enough to count backwards from as long as the last digit was a 4, since I am going to discard any digits to the left of the 4.  Suppose I had picked 34 because I know it ends with 4 and I can count backwards quite a ways from 34 -   34, 32, 30*. 30 minus 5 equal 25.  Discard the 2, since it was just a place keeper anyway and keep the 5. Write 5 under the tens of minute’s column. In the hours, 15 minus 14 minus 1 equals 0.  The answer therefore must be 0 hours and 53 minutes. 0:53”

Here’s another example:

15:06

-14:53

Say it out loud, “In the single’s column 6 minus 3 equal 3. Write 3 under the single’s minute’s column.  In the tens of minute’s column; since 5 is greater than 0, I’ll steal an hour and subtract the minutes 0, 8, 6* (or 10, 8, 6* or 20, 18, 16*…). After truncation, 6 minus 5 equal 1.  I’ll write that under the tens of minute’s column. In the hours, 14 minus 14 equal 0.  The answer therefore must be 0 hours and 13 minutes. 0:13.”

One more example:

15:01

-14:53

Say it out loud, “In the single’s column 1minus 3 equal OOPS!  3 is greater than one so, I have to steal 10 minutes from the next column.  I could steal it from the 0 and then steal an hour from the 15 hours, but that is too complicated and too easy to get lost, so instead, I’ll steal the ten minutes from the 5 by adding a small one in the tens of minutes column; making it a 0 minus 5 minus 1. I then have 11 in the single minute’s column minus 3 which is 8.  Write 8 under the single minute’s column.  Now in the tens of minute’s column I have 0 minus 5 minus 1. Since 5 is still greater than 0, I’ll steal an hour’s worth of minutes from the hours column – 0, 8, 6*.  6 minus 5 minus 1 more equal 0.  I’ll write that under the tens of minute’s column. In the hours, 15 minus 14 minus 1 equal 0.  The answer therefore must be 0 hours and 8 minutes. 0:08.”

NOTE: it is actually easy to account for the stolen 10 minutes by simply doing the usual math then counting backwards by one from the answer in the tens of minute’s column.

Here is yet another example of this process in action:

15:01

- :02

Say it out loud, “In the single’s column 2 is greater than one so, I have to steal 10 minutes from the next column.  I could steal it from the 0 and then steal an hour from the 15 hours, but that is too complicated and too easy to get lost, so instead, I’ll steal the ten minutes from the next column by adding a small one in the tens of minutes column; making it a 0 minus 1. I then have 11 in the single minute’s column minus 2 which is 9.  Write 9 under the single minute’s column.  Now in the tens of minute’s column I have 0 minus 1. Since 1 is still greater than 0, I’ll steal an hour’s worth of minutes from the hours column – 0, 8, 6*.  6 minus 1 equal 5.  I’ll write that under the tens of minute’s column. In the hours, 15 minus the one I stole equal 14 hours.  The answer therefore must be 14 hours and 59 minutes. 14:59.”

Let’s do one final problem just to make sure you’ve got it.

Here is yet another example of this process in action:

15:21

• :32

Say it out loud, “In the single’s column 2 is greater than one so, I have to steal 10 minutes from the next column.  I steal it from the 2. I then have 11 in the single minute’s column minus 2 which is 9.  Write 9 under the single minute’s column.  Now in the tens of minute’s column I have 1 minus 3 (or, 2 minus 4; or, 2 minus 3 minus 1). Since 3 is still greater than 1, I’ll steal an hour’s worth of minutes from the hours column:  1,9,7*.  7 minus 3 equal 4.  I’ll write that under the tens of minute’s column. In the hours, 15 minus the one I stole equal 14 hours.  The answer therefore must be 14 hours and 49 minutes. 14:49.”

Here’s where you can get really clever if you are careful.  Note that we did the algorithm before we did the subtraction of the ten’s of minute’s column.  That was just to make it a little more understandable. What if we stayed in base ten and did the algorithm after the subtraction?  Then in our previous example the tens of minute’s column would have been handled…

“I borrowed 10 so I need to subtract one from the ten’s of minute’s column making the 2 into a 1. Three is bigger than 1 so I’ll steal an hour and convert it to minutes…eventually.  Truncated 11, 21, 31, 41, etceteras minus 3 equal 8 then running the algorithm counting down by two twice 8, 6, 4*. I’ll write 4 under the tens of minute’s column….”  The point is that…

“Since you are only interested in the truncated value of the tens of minutes column after doing either the ‘count up by two thrice’ or the ‘count backwards by two twice’ algorithm, you can start with the representative integer plus multiples of 10 and do either algorithm before or after the subtraction to make it easier!”  Wow! Now that’s powerful.

Happy computing!

CAVEATS

• Thompsons Time add also works for minutes and seconds since 60 seconds equal a minute on the same “number base 60” as minutes and hours are also related on “number base 60”.

• Make sure you are very familiar with the concepts presented here before attempting to use them in important situations.  Remember, the mental method works every time, but you have to use it correctly.  Also, your basic mental math skills for base 10 must be tried and true.  It is very difficult to find an error in the algorithm if you’ve made a mental math error somewhere else in the equation.

• Practice, practice, practice. Practice a few minutes every day and you will become very adept at adding and subtracting time using the Thompson Time Add Mental Method very quickly and competently.  An easy way to check that you have the mental methods down correctly is to teach it to someone else.  Teaching is a great way of learning.

• Always remember that you should always check your work by reversing the calculation.  For instance, algebraically, if A - B = C, then C + B = A.

• Once you get very good at recognizing combinations of numbers you will probably start adding and subtracting numbers and time expressions starting at the left and progressing to the right instead of the usual starting on the single’s column and proceeding to the left.  If you’ve already reached this point, congratulations, math is your friend.  If not, don’t worry.  The simplest way of doing things is the way we are taught in school and occasionally less error prone.

• Finally, it should be obvious that if you use the counting backwards by 2  twice method (Alternate Method) you need to start counting backwards from a large enough number so as not to count down to a negative number...duh!

History of Captain Dave’s Time Mental Methods

I worked for approximately 10 years for commuter airlines where time sheets were written down and manually submitted for payroll and on time performance monitoring.  I remembered doing something called integer programming in college for manipulation of very large and very small numbers.  This is similar to calculations using a logarithmic scale.  The tedious adding and subtracting of time by me and fellow pilots; doing the mental gymnastics to add and subtract time in one’s head, which was already asea in performance calculations, weight and balance calculations, limitation numbers, regulation numbers, and various interpolations proved to be quite error prone.  So, I devised this method and taught it to many a new copilot.

Captain Dave’s Time Add has also been devised for Calculator manipulation of numbers.  See the article associated to this one “Captain Dave’s Time Add – Calculator Method” to learn how to do similar calculations on your calculator quickly, painlessly, and easily.

It is beyond the scope of this article to present in depth representations of all time possibilities.  More complex expressions of time that include hours minutes, seconds and days are usually better calculated on a calculator or some other computing device.   Although, mental methods can be derived for manipulating such numbers, it is often too confusing for the casual user to remember.  I have deliberately omitted them from this article to keep it simple and useful.

Captain Dave is currently, as of 2017 working as a pilot for a major airline.  He uses his Time Add methods frequently at work, in calculating flight segment times and estimated times of arrival.  On a typical transoceanic flight there may be as many as 40-50 calculations per flight to get the estimated time of arrival over various fixes or checkpoints along the route.  These calculations are done in cruising flight after the actual time of departure has been entered on the flight plan to monitor fuel burn, optimum wind economy, and forecasted winds aloft.

Captain Dave began flying at the age of 15 in southwest Kansas.  He completed his preliminary flight training and worked as a commercial pilot and flight instructor in college.

Captain Dave graduated from Wichita State University in Wichita, Kansas, USA in 1981 with a Bachelor of Science in Aeronautical Engineering. He worked in the aerospace industry for three years as an engineer before returning to a career as a professional pilot.

## Captain Dave's Time Add - Mental Method

#### *Disclaimer

As with any technology the responsibility for using it  correctly lies with the consumer.  Captain Dave, Pilotsong, BarnRocket, nor any of it's subsidiaries cannot be held liable for the misuse of these methods.  You are responsible for checking your work and/or having it checked for accuracy through other methods.

By using any  methods on this website you agree that you:

1. Fully understand how to use the methods and the underlying principals by which it functions.

2. Assume all responsibility and liability for using said methods

3. Will not hold Captain Dave, Pilotsong, BarnRocket, nor any of it's subsidiaries liable for or relating to the use of these methods.