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

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Question 24178: A plane flies 720 mi against a steady 30-mi.h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the plane's speed in the air?
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the plane's speed be x
Agianst the headwind = x-30
With the headwind = x+30
total time = 10h

720%2Fx-30+%2B+720%2Fx%2B30+=+10
720[(x-30)+(x+30)]=10[(x-30)(x+30)] --> simplify
720%5B2x%5D=10%5Bx%5E2-900%5D
1440x=10x%5E2-9000
Quardrtic equation: 10x%5E2-1440x-9000+=+0 --> divide the equation by 10
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=-%28-144%29%2B-sqrt%28%28-144%29%5E2-4%281%29%28-900%29%29%29%2F+2+x+%281%29%29 -->DIVIDE BY 2
x=144%2B-sqrt%2824336%29%29%2F+2 ---> DIVIDE by 2.
x=144%2B-156%2F%282%29
Add:
x=144%2B156%2F%282%29
x=150

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