SOLUTION: A plane travels at a speed of 220mph in still air. Flying with a tailwind, the plane is clocked over a distance of 975 miles. Flying against a headwind it takes 1 hour more time
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Question 203302: A plane travels at a speed of 220mph in still air. Flying with a tailwind, the plane is clocked over a distance of 975 miles. Flying against a headwind it takes 1 hour more time to complete the return trip. What was the wind velocity. Round to nearest tenth. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A plane travels at a speed of 220mph in still air. Flying with a tailwind, the plane is clocked over a distance of 975 miles. Flying against a headwind it takes 1 hour more time to complete the return trip. What was the wind velocity. Round to nearest tenth.
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With-the-wind DATA:
distance = 975 miles ; rate = (220+w) mph ; time = d/r = 975/(220+w) hrs
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Against-the-wind DATA:
distance = 975 miles ; rate = (220-w) mph ; time = d/r = 975/(220-w) hrs
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Equation:
time against - time with = 1 hr
975/(220-w) - 975/(220+w) = 1
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975(220+w) - 975(220-w) = (220+w)(220-w)
2(975w) = 220^2 - w^2
w^2 + 1950w - 46450 = 0
Positive solution:
w = 24.512 mph (rate of the wind)
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Cheers,
Stan H.
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