Two trains leave towns 825 mi apart at the same time and travel toward each other. One train travels 19 mi/h slower than the other. If they meet in 5 hours...

Question

what is the rate of each train?

Answer 1

Let V be the speed of the faster train and V-19 be the speed of the slower train. Then, because the two trains are heading directly at each other, their relative speed with respect to each other is:

V + (V-19) = 2V-19.

Distance covered by the two after 5 hours, is

5 * (2V-19) = 10V-95

That distance is the sum of the distances each of the trains traveled which is 825 miles since the have met. Therefore,

10V - 95 = 825

10V = 920

V = 92 (Faster train)

V – 19 = 73 (Slower train)