Question

Flying with a tailwind a plane averaged 158 km/h. On the return trip the plane averaged 112 km/h with same wind. Find wind & plane speed in still air.

Answer 1

The key idea here is that

speed of plane in wind = (speed of plane in air) + (speed of wind)

Let $s$ be the speed of the plane in still air, and $w$ the wind speed. A tailwind blows in the same direction as the plane, so for the first leg of the trip, we have

$158\,\dfrac{\rm km}{\rm h}=s+w$

For the return trip, the wind would blow in the opposite direction:

$112\,\dfrac{\rm km}{\rm h}=s-w$

Solve this system and you'll find $s=135\,\dfrac{\rm km}{\rm h}$ and $w=23\,\dfrac{\rm km}{\rm h}$.