SOLUTION: An airplane flying into a headwind travels 920 miles in 4 hours and 36 minutes. On the return flight, the distance is traveled in 4 hours. Find the airspeed of the plane and the sp

Question 297900: An airplane flying into a headwind travels 920 miles in 4 hours and 36 minutes. On the return flight, the distance is traveled in 4 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.
My dad tried to help me out on this problem, and he thinks that the answer is 200mph for the speed of the plane, and 15 mph for the speed of the wind. He wasn't sure about it and he couldn't really explain how he did it. So if you could help me out that would be great.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
An airplane flying into a headwind travels 920 miles in 4 hours and 36 minutes. On the return flight, the distance is traveled in 4 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.
My dad tried to help me out on this problem, and he thinks that the answer is 200mph for the speed of the plane, and 15 mph for the speed of the wind. He wasn't sure about it and he couldn't really explain how he did it. So if you could help me out that would be great.
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The groundspeed upwind is 920/4.6 = 200 mph
Downwind, it's 920/4 = 230 mph
The airspeed of the plane is the average of those, = 215 mph.
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The windspeed is the difference, = 15 mph
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You can do it the hard way:
a = airspeed
w = windspeed
a + w = 920/4 = 230 downwind
a - w = 920/4.6 = 200 upwind
------------------------ Add
2a = 430
a = 215
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w = 15

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