Two pipes fill a basin in 10 hrs. and 12 hrs. respectively, while a third pipe drains the filled basin in 20 hrs. If all three pipes function concurrently, how long will the basin take to fill?
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Answer: A. 7.5 hrs
Explanation
The net rate of flow is determined by adding the filling rates and subtracting the draining rate. Fractions representing hourly contributions are combined using a common denominator to find total speed. Inverting the resulting net fraction yields the exact total hours required to fill the basin. Pipe and cistern problems treat work rates as fractional parts of a tank filled per hour. Inlet pipes have positive flow rates while outlet or drain pipes have negative flow rates. The least common multiple method simplifies adding and subtracting fractional rates efficiently.
This mathematical model applies directly to municipal water treatment and reservoir management systems. Plumbing engineers use these principles to calculate pump capacities and tank filling durations. Similar calculations help determine drainage times during emergency flood control operations. Option B incorrectly estimates a faster filling time by ignoring the drain pipe effect. Option C fails to account for the precise fractional subtraction required for the drain. Option D is incorrect because the correct calculated answer of 7.5 hours is available.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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