Question

Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.

Answer 1

Answer: Let's assume that the speed of the plane in still air is represented by p and the speed of the wind is represented by w.

When the plane is flying with the tailwind, its speed relative to the ground is the sum of its speed in still air and the speed of the wind, or (p + w). Similarly, when the plane is flying against the wind, its speed relative to the ground is the difference between its speed in still air and the speed of the wind, or (p - w).

We can set up two equations based on the given information:

(p + w) = 158 (1) (when flying with the tailwind)

(p - w) = 112 (2) (when flying against the wind)

To solve for p and w, we can add equations (1) and (2):

2p = 270

p = 135

So the speed of the plane in still air is 135 km/h.

We can then substitute this value of p into equation (1) to solve for w:

(p + w) = 158

(135 + w) = 158

w = 23

So the speed of the wind is 23 km/h.

Therefore, the plane flies at 135 km/h in still air and the wind blows at 23 km/h.

Explanation: