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?

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.