Question

If a plane can travel 520 miles per hour with the wind and 420 miles per hour against the​ wind, find the speed of the plane without a wind and the speed of the wind.

Answer 1

x=speed of the plane
y=speed of the wind.
we can suggest this system of equations:

x+y=520
x-y=420

we can solve this system of equations by reduction method.

x+y=520
x-y=420
---------------
2x=940                   ⇒x=940/2=470

    x+y=520
-1(x-y=420)
----------------
     2y=100              ⇒y=100/2=50

Answer: the speed of the plane is 470 miles/hour and the speed of the wind is 50 miles/hour.