How long will it take the passenger train to overtake the freight train?

Question

A freight train leaves a station and travels north at 60 mph. One hour later, a passenger train leaves on a parallel track and travels north 65 mph.

Answer 1

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.  With such problems, there is either an equality or a relationship between the variables so we can solve the problem.  In this case, "to overtake" means the distance travelled by the two trains is the same; also, the time the second train travelled is one hour less than the time the first train travelled.

 

Let's use the fact that the distance is the same and set them equal:

      Distance of first train                     =                    Distance of second train

 D =     60t                                       =                65(t-1)

   60t = 65(t-1)            [re-write equation]

    60t = 65t - 65           [distribute]

    -5t = -65                 [subtract 65t from both sides]

      t = 13                [divide both sides by -5]

 

It will take 13 hours from the time the first train left the station (and 12 hours from the time the second train left the station) for the second train to overtake the first train.