Question

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

Answer 1

315 miles

Explanation:

let s = her speed to the mountain

s + 18 is her return speed

distance from home to mountain and mountain going back home are the same

distance equation = speed x time

7s = 5(s + 18)

7s = 5s + 90

7s - 5s = 90

2s = 90

s = 45

therefore, her speed going to the mountain is 45mph

45 x 7 = 315 mi to the mountains

let's solve the return trip

(45 + 18) x 5

63 x 5 = 315 mi