SOLUTION: A plane traveled 416 miles to Des Moines and back. The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip took 8 hours. Find the speed of the

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Question 487844: A plane traveled 416 miles to Des Moines and back. The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip took 8 hours. Find the speed of the plane in still air and the speed of the wind.
Answer by lwsshak3(11628) About Me  (Show Source):
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A plane traveled 416 miles to Des Moines and back. The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip took 8 hours. Find the speed of the plane in still air and the speed of the wind.
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Let x=speed of plane in still air
Let w=speed of wind
Speed of plane downwind=x+w
Speed of plane into wind =x-w
Travel time= distance/speed
2 Equations:
Downwind:
416/x+w=4
4x+4w=416
Into wind:
416/x-w=8
8x-8w=416
multiply first equation by 2
8x+8w=832
add first and second equations
16x=1248
x=78
Using first equation:
4x+4w=416
4w=416-4x=416-312=104
w=26
..
ans:
speed of plane in still air=78 mph
wind speed=26 mph