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.
[tex]Distance =Speed\times Time[/tex]
Substitute the respective values.
[tex]D=x\times 8\\D=8x[/tex]
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.
[tex]D =(x+21)\times 5\\D=5x+105[/tex]
Equate both the equations.
[tex]5x+105=8x\\3x=105\\x=35[/tex]
Substitute the value of x in [tex]D=8x[/tex]
[tex]D=8(35)\\D=280[/tex]
Hence, Keith live 280 miles far way from the mountains.
