SOLUTION: One plane flew 390 km with the help of a tailwind in twice the time that another plane flew 180 km against the headwind. If each plane can fly 500 km/h in still air, find the rate

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Question 107933: One plane flew 390 km with the help of a tailwind in twice the time that another plane flew 180 km against the headwind. If each plane can fly 500 km/h in still air, find the rate of the tailwind.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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One plane flew 390 km with the help of a tailwind in twice the time that another plane flew 180 km against the headwind. If each plane can fly 500 km/h in still air, find the rate of the tailwind.
:
Let x = rate of the wind:
:
(500+x) = speed with the wind
(500-x) = speed against the wind
:
Write a time equation: Time = Distance/speed
:
With time = twice against time
390%2F%28%28500%2Bx%29%29 = 2%28180%2F%28%28500-x%29%29%29
:
390%2F%28%28500%2Bx%29%29 = 360%2F%28%28500-x%29%29
:
Cross multiply:
360(500+x) = 390(500-x)
:
180000 + 360x = 195000 - 390x
:
360x + 390x = 195000 - 180000
:
750x = 15000
:
x = 15000/750
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x = 20 mph is the speed of the wind
:
:
Check solution by finding the time relationship
390/520 = .75
180/480 = .375; confirms our solution
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Did this make sense to you? Any questions?