Answer
The express train is going 70 mph, and the freight train is going 50 mph.
Work Step by Step
Recall that velocity is equal to change in distance over change in time. We call t the time it takes the express train. Thus, we obtain:
$\frac{300}{t+2} = \frac{ 280}{t} -20 $
We create common denominators and solve for t:
$ \frac{300t}{t(t+2)} = \frac{280(t+2)}{t(t+2)} + \frac{-20t(t+2)}{t(t+2)}$
Since the denominators are the same, we cancel them out and solve. (Recall, t cannot be negative.)
$300t = 280t +560 -20t^2 -40t \\ 20t^2 +60t -560 = 0 \\ 20(t+7)(t-4) \\ t = 4$
Thus, the express train went:
$ v = 280/4 = 70$
Since the freight train was 20 mph slower, it went 50 mph.
