Question 95172
A plane flies 720 miles against a steady 30m/h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the planes speed in the air?
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Let the plane's speed in still air be "p".
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Against the wind DATA:
Distance = 720 mi ; Rate = (p-30) mph ; Time = d/r = 720/(p-30)
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With the wind DATA:
Distance = 720 mi ; Rate = (p+30) mph ; Time = d/r = 720/(p+30)
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EQUATION:
time + time = 10 hr
720/(p-30) + 720/(p+30) = 10
72/(p-30) + 72/(p+30) = 1
72(p+30) + 72(p-30) = p^2-900
144p = p^2-900
p^2-144p-900 = 0
(p-150)(p+6)=0
Positive answer:
p = 150 mph (plane's speed in still air)
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Cheers,
Stan H.