let's call the speed of the airliner in still air "a" in miles per hour. when flying against the wind, its effective speed is reduced, so it travels at (a - 21) miles per hour. when flying with the wind, its effective speed is increased, so it travels at (a + 21) miles per hour.
we can use the formula: time = distance / speed.
for the first leg of the trip (against the wind), the time is 5.5 hours, and for the return leg (with the wind), the time is 5 hours. since the distance is the same for both legs of the trip, we can set up the following equations:
1. distance = (a - 21) * 5.5
2. distance = (a + 21) * 5
since both equations represent the same distance, we can set them equal to each other:
(a - 21) * 5.5 = (a + 21) * 5
now, let's solve for "a":
5.5a - 115.5 = 5a + 105
subtract 5a from both sides:
0.5a - 115.5 = 105
add 115.5 to both sides:
0.5a = 220.5
now, divide by 0.5 to find "a":
a = 441
so, the speed of the airliner in still air is 441 miles per hour.
hope this helped!