Greg drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Greg 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 Greg live from the mountains?

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jitumahi76 jitumahi76 · Answer 1 · 2020-03-27T08:19:32+01:00

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 = [tex]x+21[/tex]

Now we know that;

Distance is equal to Speed times Time.

So we can say that;

Distance while travelling the mountain = [tex]8x[/tex]

Distance while returning home = [tex]5(x+21) =5x+105[/tex]

Now we know that;

Distance while travelling the mountain and Distance while returning home will both be equal.

so we get;

[tex]8x=5x+105[/tex]

Combining like terms we get;

[tex]8x-5x=105\\\\3x=105[/tex]

Dividing both side by 3 we get;

[tex]\frac{3x}{3}=\frac{105}{3}\\\\x=35\ mi/hr[/tex]

Substituting the value of x in any of the Distance equation we get;

Distance = [tex]8x= 8\times 35 = 280\ miles[/tex]

Hence Greg lives 280 miles from the mountains.