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

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Question 95172: A plane flies 720 miles against a steady 30m/h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the planes speed in the air?
Found 2 solutions by stanbon, checkley71:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A plane flies 720 miles against a steady 30m/h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the planes speed in the air?
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Let the plane's speed in still air be "p".
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Against the wind DATA:
Distance = 720 mi ; Rate = (p-30) mph ; Time = d/r = 720/(p-30)
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With the wind DATA:
Distance = 720 mi ; Rate = (p+30) mph ; Time = d/r = 720/(p+30)
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EQUATION:
time + time = 10 hr
720/(p-30) + 720/(p+30) = 10
72/(p-30) + 72/(p+30) = 1
72(p+30) + 72(p-30) = p^2-900
144p = p^2-900
p^2-144p-900 = 0
(p-150)(p+6)=0
Positive answer:
p = 150 mph (plane's speed in still air)
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Cheers,
Stan H.

Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
720/(X+30)+720/(X-30)=10
[720(X-30)+720(X+30)]/(X+30)(X-30)=10
(720X-21600+720X+21600)/(X^2-900)=10
1440X/(X^2-900)=10 NOW CROSS MULTIPLY
10X^2-9000=1440X
10X^2-1440X-9000=0
X^2-144X-900=0
(X-150)(X+6)=0
X-150=0
X=150 MPH IS THE SPEED OF THE PLANE.
PROOF
720/180+720/120=10
4+6=10
10=10