Question 309028
Basic facts:

1. The speed of the airplane will always be greater than the wind.
2. When the airplane travels with the wind, the speed of the wind will be added to its own speed.
3. When the airplane travels against the wind, the speed of the wind will be subtracted from its own speed

Now let us try to solve the problem.

Let us take the speed of the airplane in still air as x miles/hr
We have the speed of the wind at 30 miles/hr
So when the airplane is moving in the direction of the wind the combined speed will become (x + 30)miles/hr
When the airplane is moving against the wind the combined speed will become 
(x - 30)miles/hr

Let us take the help of the formula:

TIME taken = Distance travelled / Speed

Time taken to travel with the wind = 2160/(x + 30)
Time taken to travel against the wind = 1920 / (x-30)

We know from the question that the time taken is same in both directions, hence we can form the equation:

2160/(x + 30) = 1920 / (x-30)
or, (x-30)/(x + 30)= 1920 / 2160 (cross multiplication)
or, (x-30)/(x + 30)= 8/9 (reduced to lowest terms)
or, (x-30)x 9 = 8 x (x + 30) (cross multiplication)
or, 9x - 270 = 8x + 240
or, 9x - 8x = 240 + 270 (Bringing variables to one side and numbers to the other)

or, x = 510

Hence the speed of the airplace in still air is 510 miles/hr