Two pipes P and Q fill a reservoir in 12 minutes and 16 minutes respectively. Starting both simultaneously, after what duration should Q be shut off so that the container fills completely in 9 min?
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Answer: C. 4 min
Explanation
Pipe P operates for the entire duration of nine minutes to fill a specific fraction. Subtracting P fraction from the total tank capacity leaves the exact volume required for pipe Q. Multiplying the remaining fraction by Q total filling time gives the duration before shutdown. Rates of individual pipes are expressed as reciprocal fractions of total completion time per minute. Simultaneous operation means multiple pipes contribute to the total volume concurrently. Fractional parts of a whole container always sum to one when the container fills completely.
Industrial mixing tanks often require sequential valve operations to achieve precise chemical proportions. Automated filling systems use timing mechanisms to shut off secondary supply lines dynamically. Managing fluid inflows prevents overflow and maintains accurate volumetric targets in manufacturing. Option A underestimates the duration pipe Q needs to run before being shut off. Option B results from miscalculating the fraction of the reservoir filled by pipe P. Option D overestimates the operational time required for pipe Q during the filling cycle.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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