Solving a distance, rate, time problem using a linear equation

Question

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

Do not do any rounding.

Answer 1

speed = distance/ time

s=d/t

 

On the way to the mountains his speed, s, is given by this equation:

s = d/10

 

On the way home from the mountains, his speed, s, was 18 mi/hr more, so the equation looks like this:

s+18 = d/7

 

Replace s in the second equation with d/10 from the first equation:

(d/10) + 18 = d/7 multiply both sides by 70 to get rid of the fractions:

70((d/10) + 18) = (70d)/7

(70d/10) + 1260 = (70d)/7

7d + 1260 = 10d

1260 = 3d

d = 420 miles

 

We can check. Speed on the way up:

s = 420/10 = 42 mi/hr

 

Speed on the way down:

s = 420/7 = 60 mi/hr

 

60 - 42 = 18