algebra
posted by Samantha on .
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?

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 t2 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 (t2) = d
freight train:
r x t = d, 64 x t = d
They both equal d, so they equal each other: 96 x (t2) = 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(t2).