Question 966597: Tony drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Tony drove home, there was no traffic and the trip only took 8 hours. If his average rate was 20 miles per hour faster on the trip home, how far away does Tony live from the mountains?
Do not do any rounding.
Answer by macston(5194)   (Show Source):
You can put this solution on YOUR website! .
R=rate on the way to the mountains. Since distance was the same in both directions, rate going x time going = rate returning x time returning or:
R(12 hours)=(R+20mph)(8 hours)
12R hours=8R hours + 160 miles Subtract 8R hours from each side.
4R hours=160 miles Divide each side by 4 hours.
R=40 miles/hour Tony's average speed on the way to the mountains was 40 mph.
The trip took 12 hours at 40 miles per hour, so distance was:
(12 hours)(40 mph)=480 miles
ANSWER: Tony lives 480 miles from the mountains.
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CHECK:
Return trip at 20mph faster took 8 hours:
480 miles/(40mph+20mph)=8 hours
480 miles/60 mph=8 hours
8 hours=8 hours
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