SOLUTION: A plane flies 720 miles against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 hours, what is the planes's speed in still a

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Question 33306: A plane flies 720 miles against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 hours, what is the planes's speed in still air.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Plane total distance = 720 miles:
With the wind the plane speed is: x+30
Against the wind: x-30
Total time of them both = 10h
equation:
720%2F%28x-30%29%2B720%2F%28x%2B30%29=10
720[(x-30)+(x+30)]=10[(x-30)(x+30)]
720(2x)=10(x^2-900)
10x^2-9000-1440x=0
x^2-144x-900=0
x%5E2-144x-900=0
Use quadratic formula: x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in ax%5E2%2Bbx%2Bc a=1, b=-144, c=-900
x=%28-%28-144%29%2B-sqrt%28%28-144%29%5E2-4%281%29%28-900%29%29%29%2F+2+%2A+%281%29%29 -->DIVIDE BY 2
x=%28144%2B-sqrt%2824336%29%29%2F+2 --->
x=%28144%2B-156%29%2F%282%29
Add:
x=144%2B156%2F%282%29
x=150

Hence the speed of the plane in still air is 150mi/h.
Paul.