Pipe A fills a reservoir in 5 hours, B in 10 hours, and C in 30 hours. Operating simultaneously, how many hours will it take to fill?
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Answer: C. 3
Explanation
Pipe A, B, and C fill the reservoir at individual rates of one fifth, one tenth, and one thirtieth per hour. Adding these individual fill rates together gives a combined operating rate of one third per hour. Taking the reciprocal of the combined rate determines that operating simultaneously takes exactly three hours. Pipe and cistern problems model fluid flow rates as fractional parts of a reservoir filled per unit of time. Operating multiple inflow pipes simultaneously requires summing their individual hourly fill rate fractions. The total time required to complete the filling process is the reciprocal of the sum of all active pipe rates.
Option A underestimates the total time required by miscalculating the sum of the fractional fill rates. Option B represents an intermediate estimate that does not match the exact fraction addition result. Option D overestimates the required time by assuming lower combined flow efficiency for the pipes.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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