Pipes A and B can fill a tank in 6 hours and 8 hours, respectively. Both pipes are opened together for 3 hours. After that pipe A is closed, and B continues to fill the tank. In how many hours will the tank be filled?
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Step 1: Rate of each pipe.
Pipe A fills the tank in 6 hours, so its rate is \(\frac{1}{6}\) per hour. Pipe B fills it in 8 hours, so its rate is \(\frac{1}{8}\) per hour.
Step 2: Work done together in 3 hours.
Combined rate = \(\frac{1}{6}+\frac{1}{8}=\frac{4+3}{24}=\frac{7}{24}\) per hour.
In 3 hours, filled = \(3\times\frac{7}{24}=\frac{7}{8}\) of the tank.
Step 3: Remaining work by B alone.
Remaining = \(1-\frac{7}{8}=\frac{1}{8}\). Time taken by B = \(\frac{1/8}{1/8}=1\) hour.
Step 4: Total time.
Total time = \(3+1=4\) hours.
Hence, the correct answer is 4 hours.
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