solving a distance, rate,time problem using linear equations

Question

Juan drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10

 hours. When Juan 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 Juan live from the mountains?

Do not do any rounding.

Answer 1

Here is the equation you want to be using:

(Note the symbol I use "x" for multiplication)

distance = rate x time

OR

d = rate x time

Juan's --> Mountains

d = r x 10

d = 10r

Mountains --> Juan's House

d = (r + 18) x 7

d = 7(r+18)

We know that d = 10r, so...

10r = 7(r+18)

10r = 7r + 126

10/7r = 126 --------------------- for this one, multiple both sides by 7/10

r = 88.2

Now you can figure out distance!

d = r x 10

d = 88.2 x 10

d = 882 miles

Juan lives 882 miles from the mountains