SOLUTION: the speed of an airplane in still air is 257 mph. the plane travels 570 mi against the wind and 1780 with the wind in a total time of 9 hr. what is the speed of the wind?

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Question 82147: the speed of an airplane in still air is 257 mph. the plane travels 570 mi against the wind and 1780 with the wind in a total time of 9 hr. what is the speed of the wind?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the speed of an airplane in still air is 257 mph. the plane travels 570 mi against the wind and 1780 with the wind in a total time of 9 hr. what is the speed of the wind?
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Against the wind DATA:
Distance = 570 mi ; Rate = 257-wind ; Time = d/r = 570/(257-w) hr.
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With the wind DATA:
Distance = 1780 mi ; Rate = 257+wind; Time = d/r = 1780/(257+w) hr.
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EQUATION:
time with + time against = 9 hr.
1780/(257+w) + 570/(257-w) = 9
Multiply thru by (257^2-w^2) to get:
1780(257- w) + 570(257 + w) = 9(257^2-w^2)
603950 - 1210w = 594441 - 9w^2
9w^2-1210w+9509 = 0
w = [1210 +- sqrt(1210^2-4*9*9509)]/18
w = [1210+-1059.14]/18
Positive answer: w = 126.06 mph
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Cheers,
Stan H.