SOLUTION: Raina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Raina drove home, there was no traffic and the trip only t

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Question 1040343: Raina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
12
hours. When Raina drove home, there was no traffic and the trip only took
8
hours. If her average rate was
20
miles per hour faster on the trip home, how far away does Raina live from the mountains?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
                RATE         TIME         DISTANCE
GOING            r            x            d
RETURN           r+k          t            d

system%28x=8%2Ct=12%2Ck=20%2Cr=unknownrate%2Cd=unknowndistance%29


Travel Rates Rule is RT=D relating RATE, TIME, and DISTANCE.

system%28rx=d%2C%28r%2Bk%29t=d%29

rx=%28r%2Bk%29t

rx=rt%2Bkt

rx-rt=kt

r%28x-t%29=kt

highlight_green%28r=%28kt%29%2F%28x-t%29%29

--substitute into this one:
d=rx

d=%28%28kt%29%2F%28x-t%29%29x

highlight%28d=%28kxt%29%2F%28x-t%29%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Raina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
12
hours. When Raina drove home, there was no traffic and the trip only took
8
hours. If her average rate was
20
miles per hour faster on the trip home, how far away does Raina live from the mountains?
Let distance be D

Speed to mountains: D%2F12, and speed home = D%2F8

We then get the following SPEED equation: D%2F12+=+D%2F8+-+20

2D = 3D - 480------- Multiplying by LCD, 24

2D – 3D = - 480

D, or distance = %28-+480%29%2F%28-+1%29, or highlight_green%28matrix%281%2C2%2C+480%2C+miles%29%29