Question 91810
Assume the plane speed is x, the wind speed is y

5(x + y) = 800
8(x - y) = 800

Solve this system of equations:


Multiply the first equation by 8; second equation by 5,

we have 40(x + y) = 6400
        40(x - y) = 4000

40x + 40y = 6400
40x - 40y = 4000

add these 2 equations:  80x = 10400, solve for x , x = 130
Plug x = 130 into one of the above equations to solve y:

{{{40*130 + 40y}}} = 6400

40y = 6400 - 5200

y = 30

So the speed of plane is 130, the speed of the wind is 30