Two pipes A and B fill a reservoir in 10 and 15 minutes individually. Someone activates both pipes together, but upon the expected completion time discovers a drainage pipe was left open. Shutting this drainage pipe allows the reservoir to fill completely in an extra 4 minutes. How long does the drainage pipe alone take to empty the full reservoir?
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Answer: B. 8 min
Explanation
Calculating the expected filling time without any drainage yields exactly six minutes of operation. Accounting for the extra four minutes reveals that the drainage pipe operates simultaneously throughout. The drainage pipe empties the full reservoir in exactly eight minutes based on the flow rates. Pipe A fills the entire reservoir in ten minutes at a rate of one-tenth per minute. Pipe B fills the entire reservoir in fifteen minutes at a rate of one-fifteenth per minute. Combined filling rate of both pipes equals one-sixth of the total reservoir volume per minute.
Complex fluid systems often encounter unforeseen leaks during standard municipal water treatment plant operations. Engineers calculate drainage capacities to prevent structural overflows during unexpected operational component failures. Maintenance technicians routinely inspect industrial piping networks to identify hidden blockages or drainage malfunctions. Option A suggests a duration of seven minutes which fails the mathematical balance of flow rates. Option C proposes nine minutes which contradicts the derived algebraic solution for the drainage rate. Option D implies ten minutes which neglects the combined operational timing of the filling pipes.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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