Upstream and Downstream

Question

A freight train and an AMTRAK train leave towns that are 450 miles apart and travel toward each other. They pass each other in 5 hours. The AMTRAK train travels 20 miles per hour faster that the freight train. Where do they meet?

Answer 1

Well suppose the speed of the freight train is f mph

Then the speed of the Amtrak train is f+20 mph

After 5 hours the freight train has travelled 5f miles and the Amtrak train 5 (f+20)

Sum of these distances must be 450

So 5f + 5 (f+20) = 450

f + f + 20 = 90

2f + 20 = 90

2f = 70

f = 35

So they meet 5 x 35 = 175 miles from where the freight train starts