Expert: Scott A Wilson - 9/30/2009

Question
Train A travels 12 mph slower than Train B. Train A travels 200 miles in the same time it takes Train B to travel 260 miles. The first time I did this problem I got Train A travelling at 40 mph, and train B traveling at 52 mph. The second time I did it, train A was 38 mph, and train B was 50 mph. I don't know which is right, or if either one is right.

Answer
A = velocity of train A, B = vecocity of train B.
A can travel 200 miles in the same time it takes B to go 260 miles.

This means that if the trains travel for one hour, A goes 200 and B goes 260.
This can be seen to mean that to go 2,600 miles, 13A = 10B.
This is true for any distance, but that one was chosen out of convenience.

Another way to view is is to say that A = (200/260)B, or A = (10/13)B,
which still leads to 13A = 10B.

Using the 1st answer you gave, 13(40) = 520 = 10(52), so the first one is right.
A was travelling at 40 and B was travelling at 52.

That 2nd one is not right.
For the time it would take A to go 200 miles would be 200/38 = 5 10/38 = 5 5/19 hours and
the time it would take B to go 260 miles would be 260/50 = 5 10/50 = 5 1/5.
The 1st one is just under 5 hours, 15 minutes and the second one is 5 hours, 12 minutes.