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a plane can fly 2000 miles with a tailwind in 4 hours. it can make the return trip against the same wind in 5 hours. find the speed of the plane in still air and the speed of the wind

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Andy C. | Math/Physics TutorMath/Physics Tutor
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2000 = (r+s)*4
 
2000 = (r-s)*5
 
Subtracting the 1st equation from the second:
 
 (r-s)*5 - (r+s)*4 = 0
 
5r - 5s - 4r - 4s = 0
 
r -9 s = 0
 
r = 9s
 
The plane is 9 times as fast as the wind.
 
2000 = (9s +s)* 4
2000 = 10s * 4 = 40s
 
s = 50
 
The wind is 50 mph.
The plane is 450 mph.
 
With the wind:  2000 / (450 + 50) = 2000 / 500 = 4 hours
Against the wind: 2000 / (450 -50) = 2000 / 400 = 5 hours