, how far away does Kareem live from the mountains?

Question

Kareem drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
12
hours. When Kareem drove home, there was no traffic and the trip only took
8
hours. If his average rate was
20
miles per hour faster on the trip home

Answer 1

R = rate going    12 = time going   so d = 12R

 

R + 20 = rate coming back       8 = time coming back      so d = 8(R + 20)

 

The distances going and coming back are the same so we get the equation

 

12R = 8(R + 20)          distribute

 

12R = 8R + 160           subtract 8R from both sides

 

  4R = 160                   divide both sides by 4

 

    R = 40 mph        This is the rate for the trip going

 

d = rt   To find the distance we multiply the 40 mph rate times the 12 hour time and get 480 miles

 

480 miles is the distance from the mountains 

 

We can check this by using the coming back trip

 

d = rt  The rate here would be R + 20 = 40 + 20 = 60mph

 

d = 60(8) = 480 miles the same as the going distance √