Two pipes A and B fill a water reservoir in 2 minutes and 15 minutes respectively when operated separately. Both open together, but pipe A is closed 4 minutes post-commencement. How long will filling the reservoir take?
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Answer: B. 10 min
Explanation
Calculating individual filling rates gives one-twelfth and one-fifteenth of the reservoir per minute. Running both pipes together for the initial four minutes before closing pipe A fills a specific initial fraction. Allowing pipe B to finish the remaining volume brings the total elapsed filling time to exactly 10 minutes. Time and work problems utilize unit rates expressed as fractional parts of a complete job accomplished per minute. When one contributor stops working, the remaining task must be completed solely by the active contributor. Total elapsed time is the sum of the initial joint operation phase and the subsequent solo operation phase.
Option A underestimates the total completion time required for pipe B to finish the remaining volume. Option C overestimates the total duration by miscalculating the remaining work rate contribution. Option D assumes an excessive filling time that exceeds the actual mathematical requirement of ten minutes.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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