SOLUTION: : An airplane flies 594 miles with a 30-mph tailwind and then flies back into the 30-mph wind. If the time for the round trip was four hours, find the speed of the airplane in calm

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Question 759611: : An airplane flies 594 miles with a 30-mph tailwind and then flies back into the 30-mph wind. If the time for the round trip was four hours, find the speed of the airplane in calm air.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
An airplane flies 594 miles with a 30-mph tailwind and then flies back into the 30-mph wind. If the time for the round trip was four hours, find the speed of the airplane in calm air.
let x=speed of airplane in calm air
x+30= speed of airplane with tail wind
x-30= speed of airplane with downwind
travel time=distance/speed
..
594%2F%28x-30%29%2B594%2Fx=4
LCD:x(x-30)
594x%2B594%28x-30%29=4x%28x-30%29
594x%2B594x-17820=4x%5E2-120x%29
4x^2-1308x+17820=0
x^2-327x+4455=0
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=-327, c=4455
x≈14.24 (reject)
or
x≈312.76
speed of airplane in calm air≈312.76 mph