Question 891313
<pre>
I put in some numbers.
</pre>
Amy drove to the mountains last weekend. There was heavy traffic on the way
there, and the trip took 8 hours. When Amy drove home, there was no traffic and
the trip only took 5 hours. If her average rate was 21 miles per hour faster on
the trip home, how far away does Amy live from the mountains? 
<pre>
Make this chart:

             | Distance |  rate | time
--------------------------------------
To mountains |          |       |  
To home      |          |       |  
</pre>
how far away does Amy live from the mountains?<pre>
Suppose Amy lives x miles from the mountains.

Fill in x as both distances and the times
going and coming 8 hours and 5 hours.  

             | Distance |  rate | time
To mountains |    x     |       |  8
Coming home  |    x     |       |  5

{{{matrix(1,4, "Use:",  rate,""="",distance/time) )}}}

to fill in the two rate boxes:

             | Distance |  rate | time
To mountains |    x     |  x/8  |  8
Coming home  |    x     |  x/5  |  5

The equation comes from this sentence:

</pre>>>...her average rate was 21 miles per hour faster on the trip home...<<<pre>

   {{{(matrix(4,1,
Her,rate,coming,home))}}} {{{""=""}}} {{{(matrix(6,1,
Her,rate,going,to,the,mountains))}}}{{{""+""}}}{{{(matrix(4,1,21,miles,per,hour))}}}  

{{{x/5}}} {{{""=""}}} {{{x/8}}}{{{""+""}}}{{{21}}}

Multiply through by LCD=40.

{{{8x}}} {{{""=""}}} {{{5x}}}{{{""+""}}}{{{840}}}

Subtract 5x from both sides:

{{{3x}}} {{{""=""}}} {{{840}}}

Divide both sides by 3

{{{x}}} {{{""=""}}} {{{280}}}

So Amy lives 280 miles from the mountains.

Edwin</pre>