ANSWER
The rate (speed) of the plane in still air is 840 km/hr and the rate of the wind is 110 km/hr.
Step-by-step explanation
Let the speed of the plane in still air be s.
Let the speed of the wind be w.
When flying with the wind, the airplane travels 5700 km in 6 hours.
When flying against the wind, the airplane travels 2920 km in 4 hours.
When a plane is flying with the wind, its speed is given as:
(s + w) km/hr
Speed is given as:
Speed = distance / time
The speed with wind = 5700 / 6
Speed with wind = 950 km/hr
This means that:
s + w = 950 ____(1)
When a plane is flying against the wind, its speed is given as:
(s - w) km/hr
The speed against wind = 2920 / 4
Speed against wind = 730 km/hr
This means that:
s - w = 730 ___(2)
We now have two simultaneous equations:
s + w = 950 ___(1)
s - w = 730 ____(2)
From (1):
s = 950 - w
Put that in (2):
950 - w - w = 730
950 - 2w = 730
=> 2w = 950 - 730
2w = 220
w = 220/2
w = 110 km/hr
Recall that:
s = 950 - w
s = 950 - 110
s = 840 km/hr
Therefore, the rate (speed) of the plane in still air is 840 km/hr and the rate of the wind is 110 km/hr.