Question

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?

Answer 1

d=360 miles

Donna lives 360 miles from the mountains.

Step-by-step 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