Question 445118: A plane travels at a speed of 180 mph in still air. Flying with a tailwind, the plane is clocked over a distance of 875 miles. Flying against a headwind, it takes 1 hour more time to complete the return trip. What is the wind velocity?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A plane travels at a speed of 180 mph in still air. Flying with a tailwind, the plane is clocked over a distance of 875 miles. Flying against a headwind, it takes 1 hour more time to complete the return trip. What is the wind velocity?
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With-wind DATA:
dist = 875 miles ; rate = 180+w mph ; time = 875/(180+w) hrs.
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Against-wind DATA:
dist = 875 miles ; rate = 180-w mph ; time = 875/(180-w) hrs
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Equation:
against time - with time = 1 hr
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875/(180-w) - 875/(180+w) = 1
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875(180+w) - 875(180-w) = (180^2-w^2)
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875w+875w = 180^2-w^2
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w^2 + 1750w - 180^2 = 0
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w = 18.32245...(wind speed)
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Cheers,
Stan H.
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