Question 937771
x = time with headwind
y = time with tailwind
z = helicopter speed in still air
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s = d/t
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speed in headwind:
z - 25 = 15/x
z = 15/x + 25
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speed in tailwind:
z + 25 = 15/y
z = 15/y - 25
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equate z's:
15/x + 25 = 15/y - 25
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total time:
x + y = 27/60
y = 27/60 - x
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15/x + 25 = 15/y - 25
15/x - 15/y = -50
y(15/x - 15/y = -50)
15y/x - 15 = -50y
15(27/60 - x)/x - 15 = -50(27/60 - x)
(15*27/60)/x - 15 - 15 = -50*27/60 + 50x
(15*27/60)/x = -50*27/60 + 30 + 50x
6.75/x = 7.5 + 50x
50x - 6.75/x + 7.5 = 0
50xx + 7.5x - 6.75 = 0
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the above quadratic equation is in standard form, with a=50, b=7.5 and c=-6.75
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
50 7.5 -6.75
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the quadratic has two real roots at:
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x = 0.3
x = -0.45
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the negative root doesn't fit the problem statement, so use the positive root:
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x = 0.3 hr
y = 27/60 - x
y = 27/60 - 0.3
y = 0.15 hr
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answer:
z = 15/x + 25
z = 15/0.3 + 25
z = helicopter speed in still air = 75 mph
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