Question 818371: Devante flies a plane against a headwind for 3168 miles. The return trip with the wind took 18 hours less time. If the wind speed is 9 mph, how fast does Devante fly the plane when there is no wind?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! s = d / t
d = s * t
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outbound:
3168 = (s - w)T
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return:
3168 = (s + w)(T - 18)
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(s - w)T = (s + w)(T - 18)
(s - 9)T = (s + 9)(T - 18)
sT - 9T = sT - 18s + 9T - 162
0 = -18s + 18T - 162
18T - 18s = 162
18(T - s) = 162
T - s = 9
s = T - 9
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3168 = (s - w)T
3168 = (s - 9)T
3168 = (T - 9 - 9)T
3168 = (T - 18)T
TT - 18T - 3168 = 0
T^2 - 18T - 3168 = 0
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the above quadratic equation is in standard form, with a=1, b=-18, and c=-3168
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to solve the quadratic equation, by using the quadratic formula, plug this:
1 -18 -3168
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
T = 66
T = -48
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the negative root doesn't make sense for time, so use the positive root:
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T = 66 hours
s = T - 9
s = 66 - 9
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answer:
airplane speed in calm air: s = 57 mph
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