Let the speed of the helicopter be H and the speed of the wind be W.
If the assumption is made that traveling in the direction of the wind increases the speed of the helicopter by the speed of the wind and it is given that it takes 30 minutes...
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Let the speed of the helicopter be H and the speed of the wind be W.
If the assumption is made that traveling in the direction of the wind increases the speed of the helicopter by the speed of the wind and it is given that it takes 30 minutes to complete a journey of 120 km when that is done, we have:
W + H = 120/0.5 ...(1)
When the helicopter is flying against the wind, the journey takes 10 minutes longer
H - W = 120/(40/60) ...(2)
Adding (1) and (2)
=> 2H = 120(1/0.5 + 60/40)
=> H = 60*(2 + 1.5)
=> H = 210 km/h
W = 240 - 210 = 30 km/h
The speed of the helicopter is 210 km/h and that of the wind is 30 km/h.