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?
14 min 40 sec
To determine the total time required to fill the tank, consider the following steps:
Step 1: Calculate the rates of pipes A and B.
- Pipe A can fill the tank in 15 minutes, so the rate of Pipe A = 1/15 of a tank per minute.
- Pipe B can fill the tank in 20 minutes, so the rate of Pipe B = 1/20 of a tank per minute.
Step 2: Determine the amount of tank filled in the first 4 minutes with both pipes open.
- Combined rate of pipes A and B = (1/15 + 1/20) of a tank per minute.
- To find a common denominator: LCM of 15 and 20 is 60.
- Pipe A rate = 4/60, Pipe B rate = 3/60.
- Combined rate = (4/60 + 3/60) = 7/60 of a tank per minute.
- In 4 minutes, the part of the tank filled = 4 * (7/60) = 28/60 = 7/15 of the tank.
Step 3: Determine the remaining part of the tank to be filled by Pipe B alone.
- The remaining part = 1 - 7/15 = 8/15 of the tank.
Step 4: Calculate the time taken by Pipe B to fill the remaining part of the tank.
- Pipe B fills 1/20 of the tank per minute.
- Time required = (8/15) / (1/20) = (8/15) * 20 = 32/3 minutes = 10 minutes and 40 seconds.
Step 5: Calculate the total time.
- Total time = 4 minutes + 10 minutes 40 seconds = 14 minutes and 40 seconds.
Therefore, the total time required to fill the tank is 14 minutes and 40 seconds.
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