SOLUTION: An airplane travels 400 miles against the wind in 5 hours, and makes the return trip with the same wind in 2hours. Find the speed of the wind.

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Question 231857: An airplane travels 400 miles against the wind in 5 hours, and makes the return trip with the same wind in 2hours. Find the speed of the wind.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An airplane travels 400 miles against the wind in 5 hours, and makes the return trip with the same wind in 2hours. Find the speed of the wind.
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Against the wind DATA:
distance = 400 miles ; time = 5 hrs ; rate = 400/5 = 80 mph
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With the wind DATA:
distance = 400 miles ; time = 2 hrs ; rate = 400/2 = 200 mph
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Equations:
Let "p" be speed of the plane in still air
Let "w" be speed of the wind
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p + w = 200
P - w = 80
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Add the two equations to solve for "p":
2p = 280
p = 140 mph (speed of the plane in still air)
---Substitute into P+w = 200 to solve for "w"
140 + w = 200
w = 60 mph (speed of the wind)
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Cheers,
Stan H.