An airplane flying into a headwind travels the 1920mile flyi

An airplane flying into a headwind travels the 1920-mile flying distance between two cities in 3 hours. On the return flight, the airplane travels this distance in 2 hours and 30 minutes. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

Solution

let x=speed of plane
let c=speed of wind
x-c =net speed into wind
x+c=net speed with wind
speed*travel time=distance
2 hrs and 30 min=2.5 hrs
..
(x-c)*3=1920
(x+c)*2.5=1920

3x-3c=1920

2.5x+2.5c=1920

multiply first equation by 2.5 and second equation by 3 we get
7.5x-7.5c=4800
7.5x+7.5c=5760 add equations to eliminate c
15x=10560
x=10560/15=704 mph
..
3c=3x-1920=3*704-1920=192
c=192/3=64 mph

speed of plane=704 mph
speed of wind=64 mph