Ali drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Ali drove home, there was no traffic and the trip only took 4 hours. If his average rate was 22 miles per hour faster on the trip home, how far away does Ali live from the mountains

264 miles

Explanation:

given,

time taken by Ali to drove mountain in heavy traffic = 6 hours

time taken by Ali back home, there was no traffic = 4 hours

speed of return is 22 miles per hour faster on the trip home.

let S be the speed when he was driving to mountain.

speed when he was coming back = S + 22 mi/h

we know

distance = speed x time

d₁ = 6S

d₂ = (S+22) 4

now equating both the equations

6 S = (S+22) 4

2 S = 88

S = 44 mi/h

distance = 44 x 6

= 264 miles

distance between mountain and hill is equal to 264 miles.