SOLUTION: A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed fo the plane

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Question 128084: A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed fo the plane in still air.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed of the plane in still air.
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Let the speeed of the plane in still air be "p":
With-the-wind DATA:
Distance = 500 miles; Rate = p+10 mph ; time = d/r = 500/(p+10) hrs.
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Against-the-wind DATA:
Distance = 400 miles; Rate = p-10 mph ; time = d/r = 400/(p-10) hrs.
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EQUATION:
time with = time against
500/(p+10) = 400/(p-10)
5/(p+10) = 4/(p-10)
Cross-multiply:
4p+50 = 5p-40
p = 90 mph (speed of the plane in still air)
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Cheers,
Stan H.