Final answer:
The speed of the plane in still air is 78 mph, and the speed of the wind is 26 mph, obtained by solving two equations derived from the trip with and against the wind.
Step-by-step explanation:
To find the speed of the plane in still air and the speed of the wind, we can use the concept that the speed of the plane with the wind is the airspeed plus the windspeed, and the speed against the wind is the airspeed minus the windspeed. We are given that a plane traveled 1456 miles each way to Shanghai and back. The trip there, with the wind, took 14 hours, and the trip back, against the wind, took 28 hours. Let's denote the airspeed of the plane as 'p' and the speed of the wind as 'w'.
With the wind:
Speed = 1456 miles / 14 hours = 104 mph = p + w
Against the wind:
Speed = 1456 miles / 28 hours = 52 mph = p - w
Solving these two equations simultaneously gives us:
For with the wind: p + w = 104
For against the wind: p - w = 52
Adding the above two equations, we get:
2p = 156 → p = 78 mph (Speed of the plane in still air)
Subtracting the second equation from the first, we get:
2w = 52 → w = 26 mph (Speed of the wind)
Thus, the speed of the plane in still air is 78 mph and the speed of the wind is 26 mph.