Final answer:
By setting up equations for the plane's speed with and against the wind and solving them simultaneously, we find that the rate of the plane in still air is 720 km/h and the rate of the wind is 140 km/h.
Step-by-step explanation:
To find the rate of the plane in still air and the rate of the wind, we will use the concept of relative velocity. Let's let p represent the speed of the plane in still air, and w represent the speed of the wind. When flying against the wind, the plane's effective speed is p - w and when flying with the wind, it's p + w.
The first scenario gives us the equation
1740 km = 3 hours × (p - w), which simplifies to
580 km/h = p - w. The second scenario gives us the equation
3440 km = 4 hours × (p + w), which simplifies to
860 km/h = p + w.
We can solve these two equations simultaneously. Adding them gives:
1440 km/h = 2p, which leads to p = 720 km/h. Subtracting the first equation from the second gives:
280 km/h = 2w, which leads to w = 140 km/h.
Therefore, the rate of the plane in still air is 720 km/h and the rate of the wind is 140 km/h.