Question

A passenger train leaves the train depot 2 hours after a freight train left the same depot. The freight train is traveling 20mph slower than the passenger train. Find the rate of each train, if the passenger train overtakes the freight train in threehours.

Answer 1

50 (mph) = rate of passenger train

Explanation:

Let the rate of the freight train = R

Let the rate of the passenger train be R + 30

The freight train has been traveling for 2 + 3 = 5 hours

And the passenger train has been traveling for 3 hours

And they have traveled the same distance when the passenger train overtakes the freight train

So using rate * time = distance we have that

R(5) = (R + 20) 3 simplify

5R = 3R + 60 subtract 3R from both sides

2R = 60 divide both sides by 2

R = 30 (mph) = rate of freight train

R + 20 = 50 (mph) = rate of passenger train