Two inlet spigots fill a basin in 10 minutes and 15 minutes individually, and when combined with an open drain pipe, the basin fills in 18 minutes. How long does the drain pipe take to empty the completely filled basin?
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Answer: D. 9 min
Explanation
The combined flow rate of the two inlet pipes is found by summing their individual rates. Subtracting the net combined filling rate of eighteen minutes from the inlet rate gives the drain rate. Inverting the resulting drain rate fraction determines the exact minutes needed to empty the basin. Inlet pipes contribute positive volume while drain pipes remove volume from a shared system. Work rate equations assume steady flow conditions across all connected pipes and valves. Fractions of tanks per minute provide a standardized unit for comparing conflicting fluid rates.
Plumbing system designs must account for emergency drainage capacities alongside normal filling speeds. Industrial tank maintenance relies on calculating evacuation times for safe chemical processing. Hydraulic engineering utilizes net flow rates to prevent system overflows and operational failures. Option A underestimates the time required for the drain pipe based on incorrect rate subtraction. Option B results from miscalculating the combined inlet rates before factoring the drain. Option C significantly overestimates the time needed to empty the completely filled basin.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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