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. Fernando's rate on the side roads is 9 mi/h fa

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Question 120984: 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. Fernando's rate on the side roads is 9 mi/h faster than his rate on the freeway. Write an equation to represent this problem, and then find Fernando’s rate on the side roads.
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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. Fernando's rate on the side roads is 9 mi/h faster than his rate on the freeway. Write an equation to represent this problem, and then find Fernando’s rate on the side roads.
:
Let s = speed on the side roads
Then
(s-9) = speed on the freeway
:
It says the times for each is equal, so write a simple time equation.
Time = Distance/speed
:
Sideroad time = freeway time
20%2Fs = 15%2F%28%28s-9%29%29
:
Cross multiply
20(s-9) = 15s
:
20s - 180 = 15s
:
20s - 15s = 180
:
5s = 180
:
s = 180%2F5
s = 36 mph on the side roads
:
:
Check solution by confirming that the times are equal.
Speed on the freeway = 36 - 9 = 27 mph
20/36 = 5/9 hr
15/27 = 5/9 hr