A truck traveling 45 miles per hour and a train traveling 60 miles per hour cover the same distance. The truck travels 2 hours longer than the train. How many

Question

A truck traveling 45 miles per hour and a train traveling 60 miles per hour cover the same distance. The truck travels 2 hours longer than the train. How many hours does the train travel to catch up to the truck?

Answer 1

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.  In such problems, one item is either the same or related so that we may solve the problem.  In this problem, the Distance is the same and the Time for the truck is 2 hours longer than the time for the train.

 

Let T = time for train  (since the problem asks us to find that)

 

For truck:             [D=RT]

      D = (45 m/hr)(T+2)             ["2 hours longer than train"]

For train:             [D=RT]

      D = (60 m/hr)(T)

 

Same distance D:

     45(T+2) = 60T

     45T + 90 = 60T             [distribute]

      90 = 15T                   [subtract 45T from both sides]

        6 = T       [The travels 6 hours to cover the same distance as the train.]

 

Check:

  Is 45(6+2) = 60(6)   ?

      45(8) = 60(6)   ?

       360 = 360   ?yes