Two valves A and B fill a reservoir in 15 min and 20 min respectively. Opening both valves together, valve A is closed after 4 min. What total duration is necessary to fill the basin?
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Answer: D. 14 min 40 sec
Explanation
Valves A and B fill at individual rates of one-fifteenth and one-twentieth of the basin per minute. Working together for four minutes, both valves fill a total fraction of seven-fifteenths of the reservoir. The remaining eight-fifteenths is filled by valve B alone in thirty-two thirds minutes, totaling 14 minutes and 40 seconds. Pipe and cistern problems calculate work rates as reciprocal fractions of the total time needed to fill a tank. Combined work is determined by adding individual rates together when multiple valves operate simultaneously. Remaining work is calculated by subtracting completed fractional work from the whole unity basin volume.
Option A underestimates the total time required by miscalculating the remaining duration for valve B. Option B fails to account for the exact fractional remainder filled during the solo operation phase. Option C represents an intermediate calculation time before accounting for the full combined duration.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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