How far away does she live from the mountains?

Question

Lashonda drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
10
hours. When Lashonda 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 Lashonda live from the mountains?

Answer 1

Speed (s) = Distance (d)/Time (t)

 

When Lashonda drove to the mountains, t = 10 hours

 

s = d/10

d = 10s

 

When she was coming back, her speed was 18 miles per hour faster and she reached in 7 hours

 

s +18 = d/7

d = 7(s+18)

d = 7s + 126

 

The distance she traveled was the same so, we can equate the two right hand side terms and solve for the speed

 

10s = 7s + 126

10s - 7s = 126

3s = 126

s = 126/3

s = 42

 

Now that we know that when she was driving to Lashond, her speed was 42 miles per hour, plugging this value in the first or the second equation, you can calculate the distance. 

 

1st equation

 

d = 10s

d = 10*42

d = 420 miles

 

2nd equation

 

d = 7s + 126

d= 7*42 + 126

d = 294 + 126

d = 420 miles