a plane flies 400 miles with the wind and 300 miles against

a plane flies 400 miles with the wind and 300 miles against the wind in the same length of time. If the speed of the wind is 22 mph, what is the speed of the plane in still air?

Solution

Let the speed of the plane in still air = x mph

then for with the wind:

time taken = 400/(x + 22)

and for with the wind:

time taken = 300/(x - 22)

and time taken in both condition have same:

then 400/(x + 22) = 300/(x - 22)

4/(x + 22) = 3/(x - 22)

4(x - 22) = 3(x + 22)

4x - 88 = 3x + 66

4x - 3x = 66 + 88

x = 154

So, speed of plane in still air =154 mph