Taps A, B, and C fill a tank in 12, 15, and 20 hours. With A open continuously and B and C operating on alternating hours, when will the tank be full is_______?
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Answer: C. 7 hrs
Explanation
Tap rates per hour are one twelfth, one fifteenth, and one twentieth for A, B, and C respectively. Operating tap A continuously while B and C alternate fills cumulative fractions of the tank each hour. Summing the operational fractions across the time intervals results in the tank filling in exactly seven hours. Work rate problems determine the fraction of a task completed by each participant per unit time. Alternating schedules require tracking cumulative progress hour by hour until completion. Taps working together contribute their individual flow rates simultaneously to fill a shared container.
Water treatment facility operators calculate pump schedules to manage reservoir filling and draining cycles. Industrial manufacturing plants coordinate multiple fluid intake valves to maintain consistent tank levels. Plumbing engineers design multi inlet drainage and supply systems requiring precise flow rate coordination. Option a provides an insufficient time duration because the tank is not yet fully filled. Option b represents an intermediate fractional time that fails to align with the alternating schedule. Option d overestimates the required time by assuming slower overall operational flow rates.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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