Final answer:
To find the speed of the wind and the plane's speed in still air, two equations are set up and solved based on the speeds with and against the wind. The plane's speed in still air is 277 km/h and the wind's speed is 40 km/h.
Step-by-step explanation:
The question focuses on finding both the speed of the wind and the speed of the plane in still air given the speeds of the plane flying with and against the wind. We let the speed of the plane in still air be p and the speed of the wind be w. When flying with the wind, the plane's ground speed is p + w, and when flying against the wind, the ground speed is p - w. As stated, we have:
- p + w = 317 km/h
- p - w = 237 km/h
By adding these two equations, we can solve for p to find the speed of the plane in still air. Similarly, by subtracting the second equation from the first, we can solve for w, the speed of the wind.
Add equations: (p + w) + (p - w) = 317 + 237
2p = 554 km/h
p = 277 km/h (plane's speed in still air)
Subtract equations: (p + w) - (p - w) = 317 - 237
2w = 80 km/h
w = 40 km/h (speed of the wind)