Subtracting Time

Date: 02/27/2001 at 17:55:49
From: alyssa wilson
Subject: Working backward word problem

A marathon runner crossed the finish line after running for 2 hours, 
48 minutes, and 12 seconds. She crossed the line at 9:18:12 A.M. 
At what time did the marathon start? 

I did it this way.

9  9:18:12
-  2:48:12   my answer was 6:70 minutes. 

I don't get this. My teacher said the answer was 6:30.

Date: 02/28/2001 at 12:15:14
From: Doctor Peterson
Subject: Re: Working backward word problem

Hi, Alyssa.

It sounds as if you tried to subtract as if these were just ordinary 
numbers:

      91812
    - 24812
    -------
      67000

But in working with time, place value is a little different. The 9 
stands for the number of hours, not the number of ten-thousands; and 
one hour is 60 minutes, not 100 minutes. That changes the way you 
"borrow" (regroup) when you subtract.

Here's one way to subtract times: 

  First subtract the seconds, 12 - 12 = 0. 

  Then subtract the minutes: 18 - 48 = ? 

     We can't do it, so we have to borrow from the hours. 
     That means we take one hour (changing the 9 to 8) and 
     turn it into 60 minutes (adding that to the 18). 

  Now we can subtract 48 from 78 and get 30. Here's the work:

      8 7
      / /
      9:18:12
    - 2:48:12
    ---------
      6:30:00

That gives your teacher's answer.

If you didn't quite follow that, here are some other explanations that 
I found by searching our archives for "subtract time":

  Adding and Subtracting Units of Time
  http://mathforum.org/dr.math/problems/shellie12.11.98.html   

  Calculating Timecards
  http://mathforum.org/dr.math/problems/felker.8.3.99.html   

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