Pipes P and Q fill a cistern in 18 and 24 minutes respectively. With both open initially, when must the first pipe be closed so the cistern fills in exactly 12 minutes?
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Answer: B. after 9 mins
Explanation
Pipe Q works for the entire 12 minutes to help fill the cistern completely. Pipe P contributes to the filling process for only the first 9 minutes of operation. Combining the fractional work completed by both pipes equals the whole cistern successfully. Pipe P fills the total cistern in 18 minutes at a rate of 1/18. Pipe Q fills the total cistern in 24 minutes at a rate of 1/24. The equation sets the combined work of both pipes over t minutes plus remaining Q work to one.
This type of problem models industrial processes where machinery is turned off before completion. Engineers use such calculations to optimize resource allocation and operational time in manufacturing plants. Understanding rate problems helps in planning complex multi-stage projects efficiently. Choosing 12 minutes would mean pipe P stays open for the entire duration unnecessarily. Choosing 8.5 minutes yields an insufficient amount of total water volume inside the cistern. Choosing 10 minutes results in a total calculation that exceeds the single whole cistern capacity.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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