SOLUTION: 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?

Question 120378: 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?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.

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