A certain plane flying with the wind travels 540 km in 2 hou

A certain plane flying with the wind travels 540 km in 2 hours. Later, flying against the same wind, the plane travels 690 km in 3 hours. Find the speed of the plane in still air and the speed of the boat.
A boat takes 3 hours to go 24 km upstream. It can go 36 km downstream in the same time. Find the speed of the current and the speed of the boat.

Solution

let s = plane speed in still air
let w = speed of the wind
then
(s+w) = effective speed with the wind
(s-w) = effective speed against
:
Write two distance equations: dist = time * speed
2(s + w) = 540; (with the wind)
3(s - w) = 690; (against the wind}
:
We can simplify both these equations, divide the 1st by 2 and the 2nd by 3:
s + w = 270
s - w = 230
--------------addition eliminates w, find s
2s = 500
s = 250 km/hr speed in still air
:
Find the speed of the wind:
250 + w = 270
w = 270 - 250
w = 20 km/hr speed of the wind
:
:
A boat takes 3 hours to go 24 km upstream.
It can go 36 km downstream in the same time.
Find the speed of the current and the speed of the boat.
:
Do this problem exactly the same way:
3(s - c) = 24
3(s + c) = 36