While traveling with the wind, the speed of wind adds up to that of the plane in still air and gives resultant speed, which is (1000/2) miles per hour = 500 miles per hour

Thus, while traveling against the wind, the speed of wind is reduced from that of the plane in still air and gives resultant speed, which is (808/2) miles per hour = 404 miles per hour

Adding up the resultant speeds, we obtain a speed twice that of the plane in still air, which is=(500+404)miles per hour =904 miles per hour

Thus the speed of the plane in still air is = 904/2 miles per hour = 452 miles per hour

The speed of the air must be (500-452) miles per hour = 48 miles per hour

Because subtracting this speed of air from speed of the plane in still air we get, (452-48) miles per hour = 404 miles per hour

Hence The speed of the wind is 48 miles per hour and the speed of the plane in still air is 452 miles per hour.