travel question

Question

Keiko drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Keiko drove home, there was no traffic and the trip only took 5 hours. If her average rate was 21 miles per hour faster than on the trip home, how far away does keiko live from the mountains?

Answer 1

distance = rate*time

 

On the way to the mountains:

 

    distance = rate*(8 hours)

 

On the way home:

 

    distance = (rate+ 21 mph)*(5 hours)

 

Since both distances are the same, equate them:

 

    8* rate = (rate+21)*5

    8*rate = 5*rate + 105

    3*rate = 105

    rate = 35 mph

 

Keiko's distance from the mountains, then, is:

 

    distance = rate*time

    distance = (35 mph)*(8 hours)

    distance = 280 miles