Let a denote the airplane's speed in still air, and w the windspeed.
When the plane flies against the wind, it can travel an average speed of
(4500 km) / (6 h) = 750 km/h
so that
a - w = 750 km/h
Flying with the wind, it moves at a speed of
(2910 km) / (3 h) = 970 km/h
so that
a + w = 970 km/h
Add the two equations to eliminate w and solve for a :
(a - w) + (a + w) = 750 km/h + 970 km/h
2a = 1720 km/h
a = 860 km/h
Subtract them to eliminate a and solve for w :
(a - w) - (a + w) = 750 km/h - 970 km/h
-2w = -220 km/h
w = 110 km/h
