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11 May, 19:00

Juan drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Juan drove home, there was no traffic and the trip only took 6 hours. If his average rate was 16 miles per hour faster on the trip home, how far away does Juan live from the mountains?

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  1. 11 May, 21:47
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    Answer:Juan live 384 miles from the mountains.

    Step-by-step explanation:

    Let x be the speed of Juan for trip to the mountains

    Time taken by Juan to reach the mountains=8 hours

    then distance traveled by Juan for trip to mountain = speed * time=8x ... (1)

    Time taken by Juan to reach the home = 6 hours

    Speed increased by 16 miles per hour ∴ the resultant speed to reach the home by Juan = x+16

    then distance traveled by Juan to reach the home = speed * time

    = (x+16) 6 ... (2)

    Now distance is same in both the case (1) and (2), we get

    8x = (x+16) 6

    ⇒8x=6x+96 ... (by solving brackets)

    ⇒2x=96 ... (subtracting 6x from both sides)

    ⇒x=48 ... (dividing 2 from both sides)

    Putting this value in (1), we get

    Distance traveled by Juan for trip to mountain = 8*48=384 miles.

    ∴ Juan live 384 miles from the mountains.
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