An express train travels 600 miles in the same amount of time.....?

Question

An express train travels 600 miles in the same amount of time it takes a freight train to travel 360 miles. The rate of the express train is 20 mph faster than that of the freight train. Find the rate of each train.

Answer 1

Let x be the rate of the freight train, then
x+20 = rate of the express
Remember that distance = rate x time
time, t = d/r, distance/rate by algebraic manipulation
600 = (x+20)t, or t = 600/(x+20)
360 = xt, or t = 360/x
But since t=t, then
600/(x+20) = 360/x
(x+20)(360) = 600x
360x + 7200 = 600x
240x = 7200
x = 7200/240 = 30 mph the freight
x+20 = 50 mph the express

Answer 2

600/(v+20)=360/v

or

5v=3v+60

2v=60

v1=30 mph
v2=30+20=50 mph