Question

It takes a passenger train 2 hours less time than it takes a freight train to make the trip from Central City to Clear Creek. The passenger train averages 96mi/hr while the freight train averages 64mi/hr. How far is it from Central City to Clear Creek?

Answer 1

The basic formula is rate x time = distance. Since the freight train and the passenger train are traveling the same distance, the rate x time for each train equals the other. Let t = the time for the freight train. Then t-2 would equal the time for the passenger train, since it took two hours less time to make the trip. Now you have two equations:
passenger train:
r x t = d, 96 x (t-2) = d
freight train:
r x t = d, 64 x t = d
They both equal d, so they equal each other: 96 x (t-2) = 64 x t
Now solve for t and plug in your equation to find d, the distance.

Note: don't forget to distribute the negative sign on 96(t-2).