One pipe can fill a tank in 6 minutes, while another pipe can empty the completely filled tank in 9 minutes. If both the pipes are opened together when the tank is empty, how many minutes will it take to fill one-half of the tank?
9
In 1 minute, the filling pipe fills \(\frac{1}{6}\) of the tank, and the emptying pipe empties \(\frac{1}{9}\) of the tank.
When both are open together, the net part filled in 1 minute \(= \dfrac{1}{6} - \dfrac{1}{9}\).
Taking the LCM of 6 and 9 as 18: \(\dfrac{1}{6} - \dfrac{1}{9} = \dfrac{3}{18} - \dfrac{2}{18} = \dfrac{1}{18}\) of the tank per minute.
So the full tank is filled in 18 minutes. To fill one-half of the tank, the time required \(= \dfrac{1}{2} \times 18 = 9\) minutes.
Hence, it will take 9 minutes to fill one-half of the tank.
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