SOLUTION: A light private plane can fly 120 mph in still air. Flying against the wind, the plane can fly 320 miles in the same time it requires to fly 640 miles with the wind. Find the rate

Question 668525: A light private plane can fly 120 mph in still air. Flying against the wind, the plane can fly 320 miles in the same time it requires to fly 640 miles with the wind. Find the rate of the wind.
If w represents the rate of the wind, which expression represents the time it takes the plane to travel the 640 miles with the wind?

Found 2 solutions by stanbon, lynnlo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A light private plane can fly 120 mph in still air.
Flying against the wind, the plane can fly 320 miles in the same time it requires to fly 640 miles with the wind.
Find the rate of the wind.
If w represents the rate of the wind, which expression represents the time it takes the plane to travel the 640 miles with the wind?
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Against the wind DATA:
distance = 320 miles ; rate = 120-w ; time = 320/(120-w) hrs
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With the wind DATA:
distance = 640 miles ; rate = 120+w ; time = 640/(120+w) hrs
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Equation:
time = time
320/(120-w) = 640/(120+w)
----
Divide both sides by 320:
1/(120-w) = 2/(120+w)
----
120+w = 2(120-w)
120+w = 240-2w
3w = 120
w = 40 mph (speed of the wind)
===================================
Cheers,
Stan H.
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Answer by lynnlo(4176) (Show Source): You can put this solution on YOUR website!
d=rt OR t=d/r
t=320/(120-w)
t=640/(120+w)
320/(120-w)=640/(120+w)
640(120-w)=320(120+w)
76,800-640w=38,400+320
-640w-320w=38,400-76,800
-980w=-38,400
w=-38,400/-960
the wind speed is 40 mph
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