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\,(\rm km)/(\rm h)=s+w`

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

`112\,(\rm km)/(\rm h)=s-w`

Solve this system and you'll find
`s=135\,(\rm km)/(\rm h)` and
`w=23\,(\rm km)/(\rm h)`.