One valve fills a cistern in 2 hours while a second drains it in 3 hours. How long will filling take if both remain open?
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Answer: B. 6 Hours
Explanation
The first valve fills one half of the cistern per hour while the second drains one third per hour. Subtracting the draining rate from the filling rate gives a net fill rate of one sixth per hour. Inverting the net fill rate fraction means the cistern will take six hours to fill completely. Pipe and cistern problems involve competing rates where inflows add volume and outflows remove it. Net rates are calculated by taking the difference between positive filling speeds and negative draining speeds. The time required to complete a volume task is the reciprocal of the net working rate.
Option A underestimates the total time by miscalculating the difference between the two valve speeds. Option C overestimates the time required due to an arithmetic addition error instead of subtraction. Option D implies a slower net fill rate that contradicts the calculated one sixth hourly progress.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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