SOLUTION: With a tailwind, an airlplane can fly 1440 km in 2.5 hours. On the return flight with the same wind and flying distance the flight takes 3 h. Find the rate of the plane and the rat

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Question 306590: With a tailwind, an airlplane can fly 1440 km in 2.5 hours. On the return flight with the same wind and flying distance the flight takes 3 h. Find the rate of the plane and the rate of the wind. Help please!
Answer by mananth(16946) About Me  (Show Source):
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With a tailwind, an airlplane can fly 1440 km in 2.5 hours. On the return flight with the same wind and flying distance the flight takes 3 h. Find the rate of the plane and the rate of the wind. Help please!
let the tail wind be xmph
let the airplane speed be y kmph
with tail wind the speed will be x+y kmph
distance traveled =1440 km
time taken = 1440 / x+y = 2.5
1440 = 2.5x+2.5y
.
.
Against wind the airplane speed will be y-x
time taken = 1440/ y-x = 3
1440 = 3y-3x
3(2.5x+2.5y)+2.5(3y-3x) =3*1440 + 2.5*1440
7.5x +7.5y+7.5y-7.5x=7920
15y= 7920
y=528 kmph airplane speed
x= 48 kmph wind speed