SOLUTION: During rush hour Adrianna can drive 20 miles using side roads in the same time that it takes to travel 15 miles on the freeway. If Arianna's rate on the side roads is 10mph fraste

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Question 115659: During rush hour Adrianna can drive 20 miles using side roads in the same time that it takes to travel 15 miles on the freeway. If Arianna's rate on the side roads is 10mph fraster than her rate on the freeway, find her rate on the side roads?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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During rush hour, Adriana can drive 20 miles using the side roads in the same time that it takes to travel 15 miles on the freeway. If Adriana''s rate on the side roads is 10 mph faster than her rate on the freeway, find her rate on the side roads.
:
Let s = speed on the side road.
Then
(s-10) = speed on the freeway
:
Write a time equation, Time = Distance/Speed
:
Side road time = Freeway time
20%2Fs%29 = 15%2F%28%28s-10%29%29
:
Cross multiply:
20(s-10) = 15s
20s - 200 = 15s
20s - 15s = +200
5s = 200
s = 40 on the side road
40 - 10 = 30 mph on the freeway
:
Check the times on both speeds, 40 mph and 30 mph:
20/40 = .5 hr
15/30 = .5 hrs; confirms our solution