3) flying to kampala with a tailwind a plane averaged 158 km/h. on the return trip the plane only averaged…

Explanation:

Step1: Set up equations

Let the speed of the plane in still - air be $x$ km/h and the speed of the wind be $y$ km/h. When flying with the tail - wind, the effective speed is the sum of the plane's speed in still air and the wind speed, so $x + y=158$. When flying against the wind, the effective speed is the difference between the plane's speed in still air and the wind speed, so $x - y=112$.

Step2: Add the two equations

Adding the equations $(x + y)+(x - y)=158 + 112$. Simplifying the left - hand side gives $2x$, and the right - hand side gives $270$. So, $2x=270$. Dividing both sides by 2, we get $x = 135$ km/h.

Step3: Find the speed of the wind

Substitute $x = 135$ into the first equation $x + y=158$. We have $135+y=158$. Subtracting 135 from both sides gives $y=158 - 135=23$ km/h.

Answer:

The speed of the plane in still air is 135 km/h and the speed of the wind is 23 km/h.