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

Answer:

50 (mph)    = rate of passenger train

Step-by-step 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