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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JeanaShupp JeanaShupp · Answer 1 · 2018-10-18T08:30:46+02:00

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.