Question

Dalia flies an ultralight plane with a tailwind to a nearby town in 1/3 of an hour. On the return trip, she travels the same distance in 3/5 of an hour. What is the average rate of speed of the wind and the average rate of speed of the plane?

Initial trip:
Return trip:
Let x be the average airspeed of the plane.
Let y be the average wind speed.
Initial trip: 18 = (x + y)
Return trip: 18 = (x – y)
Dalia had an average airspeed of miles per hour.
The average wind speed was miles per hour.

Answer 1

let's let the whole distance be d = rt. it's the same trip distance, so d is the same for the trip to town and the trip back.

let's also let x = the speed of the plane and y = the speed of the wind.

for the trip to town: she's on the tailwind, so add the speed of the plane + speed of wind (x+y) and multiply by the time travelled to get d = (x+y)(1/3)

on the return trip, she's going in the opposite direction, against the wind, so subtract the speed of the wind from the plane speed. same logic, d = (x-y)(3/5)

now you have two equations for d. distribute the fractions and use elimination to eliminate one of the variables, then solve for the other. then, solve for the remaining variable by plugging the known variable value into one of the equations.