Calculating Timecards

Date: 08/03/99 at 13:01:40
From: Sandy Felker
Subject: Calculating time

Hi. I hope you can help me. I calculate timecards for hours and I'm 
wondering if there is a shortcut for calculating time. For example, 
say a person arrives at 6:08 a.m. and leaves at 3:49 p.m. Is there a 
quick formula to determine how many hours that person worked?

Date: 08/03/99 at 22:02:55
From: Doctor Peterson
Subject: Re: Calculating time

Hi, Sandy.

I have an easy method and a shortcut. You can decide which is better.

Here's the standard method: 

First, deal with the AM and PM by adding 12 to the latter, converting 
them both to 24 hour time. (If the times were PM and AM, you could 
still do the same thing, adding 12 to the later time to account for 
the passing of midnight.) 

Now you want to subtract 6:08 from 15:49.

       15:49
     -  6:08
     -------
        9:41

That was too easy, because we didn't have to do any borrowing! Let's 
do another, subtracting 6:49 a.m. from 3:12 p.m. (15:12).

       15:12
     -  6:49
     -------

We can't subtract 49 from 12, so what do we do? We borrow from the 
hours, remembering that 1 hour is 60 minutes; we subtract one from the 
hours and add 60 to the minutes:

       14:72  <-- was 15 hours and 12 minutes
     -  6:49
     -------
        8:23

Now here's the shortcut, which you may find easier or harder. Break 
the time interval you want to measure into pieces, like this:

6:49 a.m. ---> 7:00 a.m. ---> 12:00 noon ---> 3:00 p.m. ---> 3:12 p.m.
          60-49           12-7
         =11 min         =5 hr            3 hr          12 min
            |              |               |              |
            |              +---------------+              |
            |                 5+3 = 8 hr                  |
            |                                             |
            +---------------------------------------------+
                             11+12 = 23 min

The total time elapsed is 8:23, as before. If you find this easier to 
do in your head, use it; if not, use the other method.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/