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](https://tex.z-dn.net/?f=Distance%20%3DSpeed%5Ctimes%20Time)
Substitute the respective values.
![D=x\times 8\\D=8x](https://tex.z-dn.net/?f=D%3Dx%5Ctimes%208%5C%5CD%3D8x)
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](https://tex.z-dn.net/?f=D%20%3D%28x%2B21%29%5Ctimes%205%5C%5CD%3D5x%2B105)
Equate both the equations.
![5x+105=8x\\3x=105\\x=35](https://tex.z-dn.net/?f=5x%2B105%3D8x%5C%5C3x%3D105%5C%5Cx%3D35)
Substitute the value of x in ![D=8x](https://tex.z-dn.net/?f=D%3D8x)
![D=8(35)\\D=280](https://tex.z-dn.net/?f=D%3D8%2835%29%5C%5CD%3D280)
Hence, Keith live 280 miles far way from the mountains.