word problem issue

Question

Joe drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Joe drove home, there was no traffic and the trip only took 5 hours. If his average rate was 18 miles per hour faster on the trip home, how far away does Joe live from the mountains?

Answer 1

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.

 

With such problems one variable is equal to or related to another variable so we can solve the problem.  Also, we may have to solve for one variable before we can find the value of the variable the problem asks us to find.

 

In this problem, the distance to the mountains is equal to the distance from the mountains.  Also, the average rate (speed) on the way home was (x+18) whereas the speed going was just x miles per hour.

 

So, 

 

    distance = rate * time

     D_TO = x*7 = D_FROM = (x+18)*5

 

  First, find x:

         7x = 5x + 90

          2x = 90

           x = 45  mph

The speed to the mountains was 45 mph; the speed from the mountains was 63 mph.

 

    D = 7*45 = 5*63      [use either to find distance]

    D = 315 miles = 315 miles