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Question 98845: Tutor,
I only have a couple of problems left that I am having trouble with could you help me with this word problem please?
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?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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