SOLUTION: an airplane flies 1449 miles against the wind and 1539 miles with the wind in a total time of 5hours. the speed of the airplane in still air is 600mph. what is the speed of the win

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Question 65322: an airplane flies 1449 miles against the wind and 1539 miles with the wind in a total time of 5hours. the speed of the airplane in still air is 600mph. what is the speed of the wind ?
Found 2 solutions by checkley71, stanbon:
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
1449/(600-X)+1539/(600+X)=5
[1449(600-X)+1539(600-X)]/(360000-X^2)=5
(869400-1449X+923400+1539X)/360000-X^2=5
1792800+90X=1800000-5X^2
5X^2+90X-7200=0
X^2+18X-1440=0
(X-30)(X+48)=0
X-30=0
X=30 REAL SOLUTION
X+48
X=-48 SOLUTION
PROOF
1449/(600-30)+1539/(600+30)=5
1449/570+1539/630=5
2.542+2.448=5
5=5
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MERRY CHRISTMAS

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
an airplane flies 1449 miles against the wind and 1539 miles with the wind in a total time of 5hours. the speed of the airplane in still air is 600mph. what is the speed of the wind ?
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Let "w" be the speed of the wind.
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Against the wind DATA:
distance=1449 miles ; rate= 600-w mph ; time= d/r = 1449/(600-w) hrs
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With the wind DATA:
distance=1539 miles ; rate=(600 + w) mph ; time= d/r = 1539/(600+w) hrs
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EQUATION:
time out + time back = 5 hrs
1449/(600-w) + 1539/(600+w) = 5 hrs
1449(600+w)+1539(600-w)=5(600^2-w^2)
1792800-90w=1800000-5w^2
5w^2-90w-7200=0
w^2-18w-1440=0
(w-48)(x+30)=0
w=48 mph (speed of the wind)
Cheers,
Stan H.