Let <em>a</em> denote the airplane's speed in still air, and <em>w</em> 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
<em>a</em> - <em>w</em> = 750 km/h
Flying with the wind, it moves at a speed of
(2910 km) / (3 h) = 970 km/h
so that
<em>a</em> + <em>w</em> = 970 km/h
Add the two equations to eliminate <em>w</em> and solve for <em>a</em> :
(<em>a</em> - <em>w</em>) + (<em>a</em> + <em>w</em>) = 750 km/h + 970 km/h
2<em>a</em> = 1720 km/h
<em>a</em> = 860 km/h
Subtract them to eliminate <em>a</em> and solve for <em>w</em> :
(<em>a</em> - <em>w</em>) - (<em>a</em> + <em>w</em>) = 750 km/h - 970 km/h
-2<em>w</em> = -220 km/h
<em>w</em> = 110 km/h
