Question

Melissa drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Melissa drove home, there was notraffic and the trip only took 5 hours. If her average rate was 21 miles per hour faster on the trip home, how far away does Melissa live from the mountains?Do not do any rounding.

Answer 1

Let

x ----> average rate on the trip home

y ----> average rate on the trip to the mountains

Remember that

The rate or speed is equal to dividing the distance by the time

speed=d/t

d=t*speed

on the trip home

d=5x -----> equation 1

on the trip to the mountains

d=8y ----> equation 2

we know that

her average rate was 21 miles per hour faster on the trip home

x=y+21 -----> equation 3

therefore

substitute equation 3 in equation 1

d=5(y+21) -----> equation 4

Equate equation 2 and equation 4 (because the distance is the same)

8y=5(y+21)

solve for y

8y=5y+105

8y-5y=105

3y=105

y=35

Find out the distance

d=8y

d=8(35)=280

The answer is 280 miles