Question

Amy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Amy drove home, there was no traffic and the trip only took 4 hours. If her average rate was 27 miles per hour faster on the trip home, how far away does Amy live from the mountains?

Answer 1

Answer:252 miles

Explanation:

Given

Amy took 7 hours while going

and it took only 4 hours on her return trip

Let $v_g$ be the average speed while going and $v_h$ is the average speed while returning.

x is the distance between the home and mountain

therefore

$\frac{x}{4}-\frac{x}{7}=27$

$x\left ( \frac{1}{4}-\frac{1}{7}\right )=27$

$x=9\times 4\times 7=252 miles$

Answer 2

Answer:

252 miles

Explanation:

We define of the equation of the Velocity:  

$V=d/t$

V: velocity (miles/hour)

d : distance(miles)

t: time (hours)

V1= Speed going to the montain= d/7

V2= Speed back home= d/4  

Because the average rate was 27 miles per hour faster on the trip home:

$V2=V1+27$

$d/4=d/7+27$

$d/4-d/7=27$

($(7d-4d)/28=27$

$3d=28*27$

$d=756/3$

$d=252 miles$