Final answer:
To ensure the tank is filled in 27 minutes, we calculate the rates at which pipes A and B fill the tank. We find a common rate and set up an equation to solve for the time pipe B should be open. Pipe B should be closed after roughly 3 minutes and 52 seconds.
Step-by-step explanation:
Two pipes A and B can fill a tank in 36 minutes and 48 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 27 minutes?
First, we find out how much of the tank each pipe can fill in one minute. Pipe A can fill 1/36th of the tank in one minute, and pipe B can fill 1/48th of the tank in one minute. When both pipes A and B are opened together, they fill 1/36 + 1/48 of the tank per minute.
To find the combined rate, we need a common denominator for the fractions, which is 144. So, the equation becomes:
(4/144) + (3/144) = 7/144 of the tank per minute
Since the tank needs to be filled in 27 minutes, when both pipes are open, they will fill 27 * (7/144), which is 27/144 * 7 = 189/144 = 1 and 45/144. However, since the tank only needs to be filled once, we will disregard the extra volume and focus on the 1 whole tank filled in 27 minutes.
Now let's calculate how long we should keep pipe B open. Let t be the time that pipe B is open. With both pipes open, the volume filled would be (1/36)t + (1/48)t.
This is equal to the volume of the tank filled in 27 minutes, so we get the equation:
(4/144)t + (3/144)t = 27/144
Combining the terms gives us (7/144)t = 27/144.
By solving for t, we get t = 27/7 which is approximately 3.86 or around 3 minutes and 52 seconds. This means pipe B should be closed after about 3 minutes and 52 seconds so that the tank is full in 27 minutes with only pipe A running for the remaining time.