Question
Two pipes, A and B, can fill a tank in 12 hours and 15
hours, respectively. Pipe A is open for 6 hours and then pipe B is also opened. After how much time will the tank be completely filled?Solution
The rate at which pipe A fills the tank is 1/12 tank/hour. The rate at which pipe B fills the tank is 1/15 tank/hour. In the first 6 hours, pipe A will fill: (6 × 1/12) = 1/2 of the tank. Now, pipe A and pipe B are working together to fill the remaining 1/2 of the tank. The combined rate of pipes A and B is: 1/12 + 1/15 = (5 + 4) / 60 = 9/60 = 3/20 tank/hour. Time taken to fill the remaining 1/2 tank is: (1/2) / (3/20) = 10/3 hours = 3 hours 20 minutes. So, the total time taken = 6 + 3 hours 20 minutes = 9 hours 20 minutes. Correct Option: d
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