Question 120519
A plane flies 720 miles against a steady 30 mph headwind and then returns to the same point with the wind, if the entire trip takes 10 hours what is the plane's speed in still air?
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Let "p" be the plane's speed in still air.
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Upwind DATA;
Distance = 720 miles ; Rate = p-30; time = d/r = 720/(p-30) hrs.
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Downwind DATa:
Distance = 720 miles ; Rate = p+30: time = d/r = 720/(p+30) hrs
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EQUATION:
time up + time down = 10 hrs
720/(p-30) + 720/(p+30) = 10
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Divide thru by 10 to get:
72/(p-30) + 72/(p+30) = 1
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Multiply thru by (p-30)(p+30)=p^2-900
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72(p+30) + 72(p-30) = p^2-900
144p = p^2-900
p^2-144p-900= 0
(p-150)(p+6) = 0
p = 150 mph (plane speed in still air is 150 mph)
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Cheers,
Stan H.