Question 925030: On a certain day, Donnie observes the wind is blowing at 8 miles per hour. A bird nesting near Donnie's house flies 3/4 mile down the road (in the direction of the wind), turns around, and returns exactly 3 minutes later. What is the airspeed of the bird? (Here, 'airspeed' is the speed the bird can fly in still air.)
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x = speed of bird in still air
y = wind speed = 8 mph
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s = d/t
t = d/s
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down wind:
td = (3/4)/(x + y)
td = (3/4)/(x + 8)
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up wind:
tu = (3/4)/(x - y)
tu = (3/4)/(x - 8)
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td + tu = 3 minutes * (1/60) hour/minute
td + tu = 1/20 hour
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(3/4)/(x + 8) + (3/4)/(x - 8) = 1/20
1/(x + 8) + 1/(x - 8) = (1/20)(4/3)
1/(x + 8) + 1/(x - 8) = 1/15
(x - 8)/((x - 8)(x + 8)) + (x + 8)/((x - 8)(x + 8)) = 1/15
((x - 8) + (x + 8))/((x - 8)(x + 8)) = 1/15
x - 8 + x + 8 = (1/15)(x - 8)(x + 8)
2x = (1/15)(x - 8)(x + 8)
2x = (1/15)(xx - 64)
(1/15)xx - 2x - (1/15)64 = 0
(0.066666666666)xx - 2x - 4.2666666666 = 0
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the above quadratic equation is in standard form, with a=0.066666666666, b=-2, and c=-4.2666666666
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
0.066666666666 -2 -4.2666666666
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the quadratic has two real roots at:
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x = 32
x = -2
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the negative root doesn't fit the problem statement, so use the positive root:
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answer:
x = speed of bird in still air = 32 mph
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