Three pipes A, B, and C fill a tank in 6 hours. After 2 hours together, C is closed, and A and B finish the rest in 7 hours. How many hours does C need alone?
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Answer: C. 14
Explanation
Pipes A, B, and C combined complete one-sixth of the tank capacity per hour of operation. After working together for two hours, they complete one-third, leaving two-thirds of the tank remaining. Subtracting the combined rate of A and B from the total three-pipe rate yields C's rate as one-fourteenth. Pipe and cistern problems treat work rates as reciprocal fractions of total task completion time required. Combined work rates of multiple pipes equal the sum of their individual hourly work rate fractions. Determining an individual pipe's rate requires subtracting the other active pipes' combined rate from total.
Option A suggests ten hours which overestimates the individual hourly flow rate required for pipe C. Option B suggests twelve hours which results from an incorrect subtraction of pipe flow rate fractions. Option D suggests sixteen hours which underestimates pipe C's flow contribution to the system.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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