Solving an Algebra Word Problem

Date: 10/11/95 at 17:41:19
From: Anonymous
Subject: Word Problems

Two members of the track team spent 18 hours in total training one 
week.  Amy spent 2 hours 20 minutes more than Becky. How long did each 
spend?

Date: 10/11/95 at 23:5:39
From: Doctor Andrew
Subject: Re: Word Problems

You could do this one by writing down two equations, but it can 
also be done more intuitively.

Suppose Amy and Becky spend the same amount of time training.

The time (18 hours), which can be drawn on a line like this:

|-------------18h-------------|

would be divided up evenly like this:

|-----Amy------|----Becky-----|


But they aren't spending the same amount of time. So how far, and 
in which direction, would you move the line seperating Amy and 
Becky in the above diagram to get a 2h 20 min difference between 
the times?

In other words you want a diagram like this:

             2h 20m
            |-------|

|----Amy------------|--Becky---|
                ^
              center

If you want to do this problem with algebra, notice that

a - b = 2 1/3   and that a + b = ?

where a is Amy's time, and b is Becky's time.

I hope this helps you out.  Good luck!

-Doctor Andrew,  The Geometry Forum