Question

Flying to Kampala with a tailwind a plane averaged 185 km/h. On the return trip the plane only averaged 143 km/h while flying back into the same wind. What is the speed of the wind and the speed of the plane while in the air?

a) Define the variables for this problem.

Answer 1

To determine the speed of the plane in still air and the wind's speed, we defined variables p for the plane's speed and w for the wind's speed. By setting up a system of equations with the given speeds with and against the wind, we calculated the plane's speed as 164 km/h and the wind's speed as 21 km/h.

Step-by-step explanation:

To solve the problem of a plane flying to Kampala with and against the wind, we must define two variables: p for the plane's speed in still air, and w for the wind's speed.

Based on the question, the plane's ground speed with the tailwind is p + w = 185 km/h, and against the wind (headwind) is p - w = 143 km/h.

We can set up two equations based on these facts:
1. p + w = 185
2. p - w = 143

To solve for p and w, we add both equations:
p + w + p - w = 185 + 143
2p = 328
p = 164 km/h

Now, we replace p in any of the equations to find w.
164 + w = 185
w = 185 - 164
w = 21 km/h

Therefore, the speed of the plane in still air is 164 km/h, and the speed of the wind is 21 km/h.