Distance from the mountain

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

Solution

On the way to the mountains

d = ?
v = ?
t = 10 hours

d = 10v


On the way home

d = ?
v + 18
t = 7 hours

d = (v + 18) x 7


The distance the house is from the mountains is the same, so we can set the two equation equal to each other


10v = (v+18) x 7

10v = 7v + 126

10v - 7v = 126

3v = 126

v = 126/3 = 42

d = (v + 18) x 7

d = (42 + 18) x 7

d = 60 x 7

d = 420

Jane lives 420 miles away from the mountains