SOLUTION: An airplane is with the wind can cover 500 miles in 2 hours. the return trip against the wind cover 2.5 hours. what is the speed of the plane? what is the speed of the air?

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Question 869585: An airplane is with the wind can cover 500 miles in 2 hours. the return trip against the wind cover 2.5 hours. what is the speed of the plane? what is the speed of the air?
Answer by lwsshak3(11628) About Me  (Show Source):
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An airplane is with the wind can cover 500 miles in 2 hours. the return trip against the wind cover 2.5 hours. what is the speed of the plane? what is the speed of the air?
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let x=speed of plane in still air
let c=speed of the wind
x+c=speed of plane with the wind
x-c=speed of plane against the wind
travel time*speed=distance
...
2(x+c)=500
2.5(x-c)=500
..
2x+2c=500
2.5x-2.5c=500
..
5x+5c=1250 (mult 1st eq by 2.5)
5x-5c=1000 (mult 2nd eq by 2.0)
add
10x=2250
x=225
2c=500-2x=500-450=50
c=25
..
speed of plane in still air=225 mph
speed of the wind=25 mph