Question

Keith drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Keith drove home, there was no traffic and the trip only took 5 hours. If his average rate was 21 miles per hour faster on the trip home, how far away does Keith live from the mountains? Do not do any rounding.

Answer 1

Answer:

Keith live 280 miles far way from the mountains.

Step-by-step explanation:

Consider the provided information.

Keith drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took  8  hours.

Let the distance is D and average rate or speed is x miles.

$Distance =Speed\times Time$

Substitute the respective values.

$D=x\times 8\\D=8x$

When Keith drove home, there was no traffic and the trip only took  5

hours. The average rate was  21  miles per hour faster on the trip home,

The average rate or speed during return is x+21 miles.

Substitute the respective values in the above formula.

$D =(x+21)\times 5\\D=5x+105$

Equate both the equations.

$5x+105=8x\\3x=105\\x=35$

Substitute the value of x in $D=8x$

$D=8(35)\\D=280$

Hence, Keith live 280 miles far way from the mountains.