Pipe A can fill a tank in 4 hours, pipe B can fill the same tank in 8 hours and pipe C can fill the same tank in 8 hours. The time taken (in hours) by them to fill half of the same tank if they operate together is:
1
Compute the per-hour fill rates. Pipe A fills \(\tfrac{1}{4}\) of the tank per hour; pipes B and C each fill \(\tfrac{1}{8}\) per hour.
Combined rate \(= \tfrac{1}{4} + \tfrac{1}{8} + \tfrac{1}{8} = \tfrac{2}{8} + \tfrac{1}{8} + \tfrac{1}{8} = \tfrac{4}{8} = \tfrac{1}{2}\) tank per hour.
Time to fill the full tank together \(= \dfrac{1}{1/2} = 2\) hours.
Time to fill half the tank \(= \tfrac{1}{2} \times 2 = 1\) hour.
Hence, the three pipes together fill half of the tank in 1 hour.
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