SOLUTION: With a tailwind, a helicopter flies 300 miles in one and one half hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopter's spee

Question 677079: With a tailwind, a helicopter flies 300 miles in one and one half hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopter's speed? What is the wind's speed?

Answer by partha_ban(41) (Show Source): You can put this solution on YOUR website!
Let the speed of helicopter = h m/h
and speed of wind = w m/h
When flying with the direction of wind, the effective speed = (h + w) m/h
In one and half (1 1/2 = 3/2) hours, the helicopter will fly = (h + w) * 3/2
Therefore, (h + w) * 3/2 = 300
or, (h + w) * 3 = 300 * 2
or, (h + w) * 3 / 3 = 600 / 3
or, h + w = 200 ... ... ... (1)
When flying against the direction of wind, the effective speed = (h - w) m/h
In 3 hours, the helicopter will fly = (h - w) * 3
Therefore, (h - w) * 3 = 300
or, (h - w) * 3 / 3 = 300 / 3
or, h - w = 100 ... ... ... (2)
By adding (1) and (2), 2h = 300
Therefore, h = 300 / 2 = 150 m/h
From (1), 150 + w = 200
or, w = 200 - 150
Therefore, w = 50 m/h
So, the speed of helicopter = 150 m/h and that of wind = 50 m/h
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