Word Problems

Question

On a trip, a motorist drove 150 miles in the morning and 50 miles in the afternoon. His average rate in the morning was twice his average rate in the afternoon. He spent 5 hours driving. Find his average rate on each part of the trip.

Answer 1

 

Let "x" represent the rate for the afternoon trip.

Since the morning trip was at twice the rate of the afternoon trip, "2x" is the rate for the morning trip

 

Let "t" represent the time for the afternoon trip.

Since the total trip was 5 hours, "5 - t" represents the time for the morning trip.

 

Now we organize the data in a table, using the "RATE X TIME = DISTANCE" formula

 

 

 

                          RATE    |      TIME       |    DISTANCE

                       ----------------------------------------------------

                       |              |                    |                       |

    Morning    |    2x      |     (5 - t)      |   150 miles   |

                       |              |                    |                       |

                       ----------------------------------------------------        

                       |              |                    |                      |

   Afternoon  |      x      |         t          |    50 miles   |

                       |              |                    |                      |

                       ----------------------------------------------------

 

 

For the morning portion of the trip,

     RATE X TIME = DISTANCE

           2x(5 - t) = 150

           10x -2xt = 150

 

For the afternoon trip,

     RATE X TIME = DISTANCE

                  x(t) = 50

                    xt = 50

 

since "xt" = 50, we can substitute that into the morning equation, and then solve for x.

 

        10x - 2xt = 150

      10x -2(50) = 150

        10x - 100 = 150

                 10x = 250

                     x = 25

 

Thus, the rate for the afternoon trip is "x", which is 25 miles per hour.

The rate for the morning trip is twice the rate of the afternoon trip, so that is 50 miles per hour.