Pipe A fills a reservoir in 6 hours, but a base leak extends this to 9 hours. How long will the leak take to empty the full reservoir independently?
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Answer: C. 18 hours
Explanation
Pipe A fills the reservoir at a rate of one sixth of the tank per hour. Operating with the base leak, the net fill rate slows down to one ninth of the tank per hour. Subtracting the net rate from the pipe rate reveals the leak empties the reservoir at one eighteenth per hour. Tank filling problems with leaks treat outflow as a negative rate subtracted from the positive inflow rate. Net work or flow rate equals the gross input rate minus the active drainage or leakage rate. The reciprocal of the isolated leak rate determines the exact time required to empty a full reservoir.
Option A suggests sixteen hours, which fails to match the precise fractional subtraction of the flow rates. Option B represents fifteen hours, resulting from an incorrect calculation of the net operating speed. Option D suggests seventeen hours, which is an arithmetic error not supported by the rate difference.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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