Question 98845
A plane flies 720 mi against a steady 30 mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane's speed in stil air? 
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Let plane speed in still air be "P".
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With wind DATA:
distance = 720 miles; rate = p+30 mph ; time = d/r = 720/(p+30)
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Against wind DATA;
distance = 720 miles ; rate = p-30 mph ; time = d/r = 720/(p-30)
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EQUATION:
time + time = 10 hrs
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.