SOLUTION: During rush hour, Fernando can drive 20 miles using the side roads in the same time that it takes to travel 15 miles on the freeway. If Fernando's rate on the side road is 9 miles/

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Question 31486: During rush hour, Fernando can drive 20 miles using the side roads in the same time that it takes to travel 15 miles on the freeway. If Fernando's rate on the side road is 9 miles/hour faster than his rate on the freeway, find his rate on the side road.

Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
Hello!
The speed is measured as distance%2Ftime. Let's call X to the time he takes to drive 20 miles in the side roads (which is the same as the time he takes to drive 15 miles on the freeway). The nwe have:
Speed on side road = 20%2FX
Speed on freeway = 15%2FX
But we also know that his speed on the side road is 9 mph faster than the one on the freeway. So we get the equation:
20%2FX+=+15%2FX+%2B+9
Multiplying both sides by X in order to get rid of the X in the denominator:
20+=+15+%2B+9X
5+=+9X
X+=+5%2F9
We have that he takes 5/9 hour in order to drive 20 miles on the side road. Therefore, his speed must be:
20%2F%285%2F9%29+=+36
His speed on the side road is 36 mph

I hope this helps!
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