Let u = the aircraft speed at no wind and v = the speed of the wind.


Then the speed of the aircraft flying with the wind is (u+v) miles per hour,

while its speed flying against the wind is (u-v) miles per hour.


From the condition, you have these equations


    u + v =  = 180  mph     (1)

    u - v =  =  90  mph     (2)


Subtract eq(2) from eq(1). You will get


    2v = 180 - 90 = 90 mph

     v            = 90/2 = 45 mph.


ANSWER.  The speed of the wind is 45 miles per hour.