Pipes A and B fill a reservoir in 5 and 6 hours respectively, while C drains it in 12 hours. Operating all three simultaneously, in what time will the tank be filled?
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Answer: C. 3 9/17 hours
Explanation
Filling pipes a and b contribute rates of one fifth and one sixth per hour. Draining pipe c removes one twelfth of the tank volume every hour. Combining these rates yields a net filling speed that completes the tank in three and nine seventeenths hours. Pipes operating simultaneously combine filling and draining rates algebraically. Draining mechanisms subtract from net volume accumulation over elapsed time periods. Fractions convert into mixed time units to describe reservoir filling durations accurately.
Plumbing engineers calculate reservoir fill and drain times for water management systems. Industrial facility designers size intake and outflow valves for large storage tanks. Municipal water authorities manage pumping schedules using net flow rate equations. Option A underestimates total filling time due to an incorrect rate subtraction. Option B miscalculates the net combined flow rate for pipes and drains. Option D overestimates the time required by ignoring drainage contributions.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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