distance from mountains?

Question

Teresa drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
12 hours. When Teresa drove home, there was no traffic and the trip only took 8 hours. If her average rate was
20 miles per hour faster on the trip home, how far away does Teresa live from the mountains?
Do not do any rounding.

Answer 1

The distance formula is distance = rate * time

Going to the mountain:  d = r * 12

Going home: d = (r + 20) * 8

The distances to and from the mountains are equal, so the two expressions can be set equal.

r * 12 = (r + 20) * 8

12r = 8r + 160

Subtract 8r from each side.

4r = 160

Divide by 4

r = 40 miles per hour, when going to the mountain

40 + 20 = 60 miles per hour, when coming home

 

Checking the answers..... d = r * 12 = 40 * 12 = 480 miles

                                     d = 60 * 8 = 480 miles

 

Hope the explanation was clear, Chance.

Mary Ann