Question

A plane can fly a certain distance in 6 hours with the wind, but can return only three-fourths the distance in the same time. If the speed of the plane in still air is 200 km per hour, find the velocity of the wind.

Answer 1

let the speed of the wind be x km/h
so distance with the wind = 6(200+x) km
distance against the wind = 6(200-x)

but 6(200-x) = (3/4)(6(200+x))

solve for x , let me know what you get.

Answer 2

to the solution, x (the speed of the wind) is 200/7. But to the answer key it is 80 km/h. I am really confused :/

Answer 3

28.57 km/h

Answer 4

The speed of the wind is indeed 200/7 or 28.57 mph

check:
with the help of the wind the plane is moving at
228.57 mph, for 6 hrs = 1371.43 kkm
against the wind, the plane is moving at 200-28.57 or 171.43 km/h, and for 6 hours that would be 1028.57
and (3/4)(1371.43) = 1028.57

Your answer key of 80 km/h is incorrect

Answer 5

Thanks a lot. I will tell my teacher about this. I spent hours trying to solve this. I feel tricked :)