Bill drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Bill drove home, there was no traffic and

Question

Bill drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
10
hours. When Bill drove home, there was no traffic and the trip only took
7
hours. If his average rate was
18
miles per hour faster on the trip home, how far away does Bill live from the mountains?

Answer 1

distance=rate*time

d=rt

d=r*10

d=(r+18)*7

equate the two right sides because they both equal the same distance d

10r=7(r+18)

10r=7r+126

10r-7r=126

3r=126

r=126/3

r=42 mph driving to the mountains

d=42*10=420 miles from home to the mountains

check: 420=(42+18)*7, 420=60*7, 420=420 miles (driving home)