two pipes a and b can fill a tank in 15 minutes and 20 minutes respectively. both the pipes are opened together but after 4 minutes, pipe a is turned off. what is the total time required to fill the tank?
LectureNotes said two pipes a and b can fill a tank in 15 minutes and 20 minutes respectively. both the pipes are opened together but after 4 minutes, pipe a is turned off. what is the total time required to fill the tank?
Answer:
Let’s first find the rate at which each pipe fills the tank.
Pipe A fills \frac{1}{15} of the tank in 1 minute.
Pipe B fills \frac{1}{20} of the tank in 1 minute.
When both pipes are open for 4 minutes, together they fill (\frac{1}{15} + \frac{1}{20}) \times 4 = \frac{7}{12} of the tank.
This means after 4 minutes, the fraction of the tank left is 1 - \frac{7}{12} = \frac{5}{12}.
From this point, only Pipe B is filling the remaining \frac{5}{12} of the tank.
Since Pipe B fills \frac{1}{20} of the tank in 1 minute, it will take \frac{\frac{5}{12}}{\frac{1}{20}} = 25 minutes for Pipe B to fill the rest of the tank.
Therefore, the total time required to fill the tank is 4 minutes (when both pipes are open) + 25 minutes (when only Pipe B is filling) = 29 minutes.
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