Let the speed of the wind in km/ hr = S
The total flight time [ in hours] with the wind =T1 = D/R = 990 / (600 + S)
The total flight time [ in hours ] against the wind = T2 = 990 / (600 - S)
And the total flight time for both trips = Tt = 3 hrs, 20 min = 3 + 1/3 hrs = 10/3 hrs ......so
T1 + T2 = Tt
990 / (600 + S) + 990 / (600 - S) = 10/3 simplify ..... multiply through by 3
2970 / (600 + S) + 2970 /( 600- S) = 10
[2970 (600 - S) + 2970(600 + S) ] / [ (600 + S) (600 - S) ] = 10 cross-multiply
]2970 (600 - S) + 2970(600 + S) ] = 10 [ (600 + S) (600 - S) ]
2970 * 600 * 2 = 10 (360,000 - S^2) divide both sides by 10
297*1200 = 360,000 - S^2 rearrange
S^2 = 360,000 - 297*1200
S^2 = 3600 take the positive square root of both sides
S = 60km / hr