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.
