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.

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: