SOLUTION: A plane flies 300 miles having a tail wind of 10 mph and returns against a tail wind of 20 mph. Find the speed of the plane in still air if the time of the flight is 4.5 hours.

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Question 885698: A plane flies 300 miles having a tail wind of 10 mph and returns against a tail wind of 20 mph. Find the speed of the plane in still air if the time of the flight is 4.5 hours.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A plane flies 300 miles having a tail wind of 10 mph and returns against a tail wind of 20 mph. Find the speed of the plane in still air if the time of the flight is 4.5 hours.
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let x=speed of plane in still air
(x+10)=speed of plane with tail wind
(x-20)=speed of plane against the wind
travel time=distance/speed
300%2F%28x%2B10%29%2B300%2F%28x-20%29=4.5
300(x-20)+300(x+10)=4.5(x-20)(x+10)
300x-6000+300x+3000=4.5(x^2-10x-200)
600x-3000=4.5x^2-45x-900
4.5x^2-645x+2100=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=4.5, b=-645, c=2100
ans:
x=3.33 (reject)
or
x=140
speed of plane in still air=140 mph