Question 134490
Let x=number of gal used by angel
Then 32x=distance morgan run-clinton
And let y=number of gal used by mos
Then 22y also equals distance morgan run-clinton

So, our equation to deal with is:

32x=22y or
16x=11y  divide each side by y(not equal to zero) and 16

x/y=11/16

What this tells us is that the ratio of the number of gal used by angel and the number of gal used by mos is 11/16 and this fraction cannot be reduced further which means that this represents the smallest amount of gas that each can use that satisfies the problem.

Closest distance between morgan run and clinton
32*11 or 22*16=352 mi
Amount of gas used by angel=11 gal
Amount of gas used by mos=16 gal

You can check this problem by verifying that there are not any pairs of numbers smaller than 11 and 16 that works: For example:

If x=1, then 16=11y--------------no
If x=2, then 32=11y-----------no
etc up to x=11


Hope this helps---ptaylor