Let x be the airspeed of the plane (in miles per hour), and
let y be the speed of the wind.


Then the effective speed of the plane flying with the wind is (x+y) miles per hour,
while its speed flying against the wind is (x-y) mph.


From the condition, the effective speed with the wind is   = 540 mph.

The effective speed against the wind is   = 450 mph.


It gives you two equations


x + y = 540    (1)
x - y = 450    (2)


To solve the system, add the equations. You will get

2x = 540+450 = 990  ====>  x = 990/2 = 495.


Answer.  The airspeed of the plane is  495 mph.