SOLUTION: Felipe drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Felipe drove home, there was no traffiand the trip only took

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Question 1112541: Felipe drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Felipe drove home, there was no traffiand the trip only took 7hours. If his average rate was 18miles per hour faster on the trip home, how far away does Felipe live from the mountains?
Found 3 solutions by mananth, josgarithmetic, greenestamps:
Answer by mananth(16946)   (Show Source):
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To mountains x mph
From mountains 18 mph faster
returning speed x + 18
returning time = 7 hours
going out time= 10 hours

Distance = same
10 x = 7 ( x + 18 )
10 x = 7 x + 126
10 x - -7 x = 126
3 x = -50 126
/ 3
x = 42 mph

Returning speed=60 mph
Distance = 42*10 =420 miles
OR
Distance = (42+18) * 7= 420 miles

Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website!

SPEEDS TIMES DISTANCE GOING r 10 d=10r RETURN r+18 7 d=7(r+18)

The question asks for d.

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Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

There are all kinds of variations on how to solve a problem like this; so far you have received two good answers from other tutors.

Here is a way I like to solve problems like this; for me the required thought process and the required arithmetic is a bit easier than other methods. Try this method and see if it "works" for you.

The distances going and returning are the same; so if the ratio of times is 10:7 then the ratio of speed is 7:10. Since the higher speed is 18mph higher than the lower,

The lower speed is 42mph; the higher speed is 42+18 = 60mph.

The question asks how far Felipe lives from the mountains; you can find that distance either with 42*10 = 420 or with 60*7 = 420.