Answer: the speed of the plane in still air is 81 mph.
the speed of the wind is 27 mph.
Explanation:
Let x represent the speed of the plane in still air.
Let y represent the speed of the wind.
The trip there was with the wind. It means that total speed at which the plane travelled with the wind is
(x + y) mph.
It took 3 hours and the distance travelled was 324 miles.
Distance = speed × time
Distance travelled with the wind is
324 = 3(x + y)
Dividing both sides of the equation by 3, it becomes
108 = x + y-- - - - - - - - -1
The trip back was into the wind. It means that total speed at which the plane travelled into the wind is
(x - y) mph.
It took 6 hours and the distance travelled was also 324 miles.
Distance travelled into the wind is
324 = 6(x - y)
Dividing both sides of the equation by 6, it becomes
54 = x - y-- - - - - - - - -2
Adding equation 1 to equation 2, it becomes
162 = 2x
x = 162/2
x = 81
Substituting x = 81 into equation 1, it becomes
108 = 81 + y
y = 108 - 81
y = 27