Answer: the speed of the plane in still air is 135 miles per hour
the speed of the wind is 15 miles per hour
Explanation:
Let x represent the speed of the plane in still air
Let y represent the speed of the wind.
The distance travelled by the plane is 600 miles.
Distance travelled = speed × time
It takes the plane 5 hours against the wind. This means that the total speed is (x-y) miles per hour. Therefore,
600 = 5(x- y) = 5x - 5y - - - - - - - 1
It takes the plane 4 hours with the wind. This means that the total speed is (x+y) miles per hour. Therefore,
600 = 4(x+ y) = 4x + 4y - - - - - - - - 2
Multiplying equation 1 by 4 and equation 2 by 5, it becomes
2400 = 20x - 20y
3000 = 20x + 20y
Adding both equations
5400 = 40x
x = 5400/40 = 135
Substituting x = 135 into equation 1, it becomes
4 × 135 + 4y = 600
540 + 4y = 600
4y = 600 - 540 = 60
y = 60/4 = 15