Final answer:
By calculating the net rate at which the tank is being filled when both pipes are opened together, it is determined that Pipe B should be closed after 14 minutes to ensure that the tank is filled in 30 minutes.
Step-by-step explanation:
To find out after how many minutes pipe B should be closed in order for the tank to fill in 30 minutes when both pipes A and B are opened together, we need to calculate the rate at which the tank is filled and emptied.
Pipe A fills the tank at a rate of 1/16 of the tank per minute, while Pipe B empties the tank at a rate of 1/24 of the tank per minute. When both pipes are open together, the net rate at which the tank is filled is (1/16 - 1/24) of the tank per minute. By finding a common denominator, which is 48, we get the combined rate as (3 - 2)/48, which simplifies to 1/48 of the tank per minute.
If the tank has to be full in 30 minutes with both pipes open, Pipe B must be closed in such a way that the remaining work needed to fill the tank after B is closed, can be done by Pipe A alone in the remaining time. Since Pipe A fills 1/16 of the tank per minute, it would finish the job in 16 minutes if it were the only pipe open. Therefore, Pipe B should be closed at 30 - 16 = 14 minutes.