SOLUTION: An airplane flies 500 miles against a headwind of 40 miles per hour. The plane took 20 minutes longer for this flight that would have been the case in the still air. How fast could

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Question 997498: An airplane flies 500 miles against a headwind of 40 miles per hour. The plane took 20 minutes longer for this flight that would have been the case in the still air. How fast could the airplane travel in still air?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An airplane flies 500 miles against a headwind of 40 miles per hour.
The plane took 20 minutes longer for this flight that would have been the case in the still air.
How fast could the airplane travel in still air?
:
let s = plane speed in still air
:
Change 20 min to 1%2F3 hr
:
Write a time equation; time = dist/speed
Time against the wind - time in still air = 20 min
500%2F%28%28s-40%29%29 - 500%2Fs = 1%2F3
multiply equation by 3s(s-40), cancel the denominators and you have
3s(500) - 3(s-40)*500 = s(s-40)
1500s - 500(3s - 120) = s^2 - 40s
1500s - 1500s + 60000 = s^2 - 40s
A quadratic equation
s^2 - 40a - 60000 = 0
use the quadratic formula: a=1; b=-40; c=-60000
I got a positive solution of
s = 265.764 mph in still air