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### 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

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/
```
Associated Topics:
Elementary Calendars/Dates/Time
Elementary Subtraction
Middle School Calendars/Dates/Time

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