Answer:
Greg lives 280 miles from the mountains.
Step-by-step explanation:
Given:
Time required to drive to the mountains = 8 hours.
Time required to drive home = 5 hours.
We need to find the distance Greg live from the mountains.
Solution:
Let the average rate while driving to the mountains be 'x'.
So rate while returning home = ![x+21](https://tex.z-dn.net/?f=x%2B21)
Now we know that;
Distance is equal to Speed times Time.
So we can say that;
Distance while travelling the mountain = ![8x](https://tex.z-dn.net/?f=8x)
Distance while returning home = ![5(x+21) =5x+105](https://tex.z-dn.net/?f=5%28x%2B21%29%20%3D5x%2B105)
Now we know that;
Distance while travelling the mountain and Distance while returning home will both be equal.
so we get;
![8x=5x+105](https://tex.z-dn.net/?f=8x%3D5x%2B105)
Combining like terms we get;
![8x-5x=105\\\\3x=105](https://tex.z-dn.net/?f=8x-5x%3D105%5C%5C%5C%5C3x%3D105)
Dividing both side by 3 we get;
![\frac{3x}{3}=\frac{105}{3}\\\\x=35\ mi/hr](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B3%7D%3D%5Cfrac%7B105%7D%7B3%7D%5C%5C%5C%5Cx%3D35%5C%20mi%2Fhr)
Substituting the value of x in any of the Distance equation we get;
Distance = ![8x= 8\times 35 = 280\ miles](https://tex.z-dn.net/?f=8x%3D%208%5Ctimes%2035%20%3D%20280%5C%20miles)
Hence Greg lives 280 miles from the mountains.