A pipe can fill an empty tank in 5 minutes and another pipe can empty it in 6 minutes. If both pipes are opened simultaneously, how long will it take to fill the tank?

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Step 1: Calculate the filling rate of the first pipe: It fills the tank in 5 minutes, so its rate is 1/5 tank per minute.
Step 2: Calculate the emptying rate of the second pipe: It empties the tank in 6 minutes, so its rate is 1/6 tank per minute.
Step 3: When both pipes are open simultaneously, the net filling rate = filling rate - emptying rate = (1/5) - (1/6) = (6/30) - (5/30) = 1/30 tank per minute.
Step 4: Time taken to fill the tank = 1 / (net filling rate) = 1 / (1/30) = 30 minutes.
Therefore, the tank will be filled in 30 minutes when both pipes are opened simultaneously.

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