SOLUTION: It takes a plane 5 hours to travel 3000 miles with a tailwind, but it takes the same plane 6 hours to travel the same distance with a headwind. What is the speed of the plane in st

Question 61803: It takes a plane 5 hours to travel 3000 miles with a tailwind, but it takes the same plane 6 hours to travel the same distance with a headwind. What is the speed of the plane in still air and the speed of the wind?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
It takes a plane 5 hours to travel 3000 miles with a tailwind, but it takes the same plane 6 hours to travel the same distance with a headwind. What is the speed of the plane in still air and the speed of the wind?
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Let plane speed be p and wind speed be w.
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With the wind DATA:
distance = 3000 mi ; time=5 hrs ; rate= d/t= 600 mph
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Against the wind DATA:
distance = 3000 mi ; time= 6 hrs; rae = d/t = 500 mph
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EQUATION:
p+w=600 mph
p-w=500 mph
Add the wo quations to get:
2p=1100
p=550 mph (plane's speed in still air)
Substitute to solve for w, as follows:
550+w=600
w=50 mph (wind's speed)
Cheers,
Stan H.

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