Answer:
The speed in still air = 200 mph.
Step-by-step explanation:
21.
If the speed of the plane in still air is x mph then with the wind its speed is x+20 mph and against the wind it is x - 20 mph. Also let t hours be the time taken for the journey with the wind.
So we have the 2 equations:
x + 20 = 396 / t
x - 20 = 396 / (4 - t)
Subtracting to eliminate x
40 = 396 / t - 396 / (4 - t)
40t(4 - t) = 396(4 - t) - 396t
160t - 40t^2 = 1584 - 396t - 396t
-40t^2 + 952t - 1584 = 0
Dividing through by 8:
-5t^2 + 119t - 198 = 0
Using the quadratic formula we get t = 22, 1.8 hours . We ignore the 22 because the total time is 4 hours.
So the speed x = is found by plugging in t 1.8:
x + 20 = 396/1.8
x = 200 mph.
