Donna drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Donna drove home, there was no traffic and the trip only took 4 hours. If her average rate was 45 miles per hour faster on the trip home, how far away does Donna live from the mountains?

d=360 miles

Donna lives 360 miles from the mountains.

Explanation:

Conceptual analysis

We apply the formula to calculate uniform moving distance[

d=v*t Formula (1)

d: distance in miles

t: time in hours

v: speed in miles/hour

Development of problem

The distance Donna traveled to the mountains is equal to the distance back home, equal to d, then, we pose the kinematic equations for d, applying formula 1:

travel data to the mountains: t₁ = 8 hours, v=v₁

d = v₁*t₁=8*v₁ Equation (1)

data back home : t₂=4hours, v=v₂=v₁+45

d=v₂*t₂ = (v₁+45) * 4=4v₁+180 Equation (2)

Equation (1) = Equation (2)

8*v₁=4v₁+180

8*v₁-4v₁=180

4v₁=180

v₁=180:4=45 miles/hour

we replace v₁=45 miles/hour in equation (1)

d=8hour*45miles/hour

d=360 miles