Three pipes , , and can fill a tank in , , and hours respectively. Pipe is kept open all the time, while pipes and are opened alternately for hour each, starting with pipe . In how many hours will the tank be completely filled?
Answer and explanation
Correct answer: C. 7 hours
- Step 1: Find the total tank capacity using . The individual filling rates are: , , and .
- Step 2: In each -hour alternating cycle: hour 1 has pipes and open, delivering ; hour 2 has pipes and open, delivering . Together, are filled per -hour cycle.
- Step 3: After full cycles ( hours), are filled, leaving . In the hour, pipes and work and fill exactly . Thus, total time is .
Answer
7 hours.
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