SOLUTION: Rita drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Rita drove home, there was no traffic and the trip only took 6 h

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Rita drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Rita drove home, there was no traffic and the trip only took 6 h      Log On


   

Question 1167349: Rita drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Rita drove home, there was no traffic and the trip only took 6 hours. If her average rate was 16 miles per hour faster on the trip home, how far away does Rita live from the mountains?
Found 2 solutions by Boreal, josgarithmetic:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
lives x miles away.
x mph going there *8 hours=8x miles
(x+16) mph coming back *6 hours =6x+96 miles
both 8x and 6x+96 are equal, since it is the same trip
so 2x=96 and x=48 mph and 384 miles to the mountains.
64 mph on the way back *6 hours is 384 miles.

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
                SPEED          TIME     DIST.
GOING           d/8              8       d
RETURNING       d/6=d/8+16       6       d

d%2F6-d%2F8=16
mult. left&right by 24
4d-3d=24%2A16
highlight%28d=384%29