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?

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.

16 is the absolute value

step-by-step explanation: