Two valves fill a basin in 18 minutes and 15 minutes, whereas an extraction valve empties it in 45 minutes. Activating all valves simultaneously on an empty basin, how many minutes will be required to fill it?
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Answer: D. 10
Explanation
The net rate combines the individual filling fractions and subtracts the extraction valve rate. Adding one-eighteenth and one-fifteenth then subtracting one-forty-fifth yields one-tenth per minute. Reciprocating the net rate of one-tenth per minute determines the total filling time of ten minutes. Valve rates represent the fraction of the basin volume filled or emptied during each single minute. Finding a common denominator simplifies the addition and subtraction of fractional fluid flow rates. Working with simultaneous fluid flows requires balancing positive inlet streams against negative outlet streams.
Civil engineers design municipal water reservoirs by balancing active inflow sources against emergency drainage outlets. Industrial chemical processing tanks rely on precise valve synchronization to maintain stable fluid levels safely. Agricultural irrigation systems utilize multiple pumps and drains to regulate water distribution across fields. Option A suggests twelve minutes which overestimates the time required for the balanced flow rates. Option B proposes thirteen minutes which fails to match the precise fraction calculated from the valve rates. Option C implies eleven minutes which misjudges the combined net efficiency of the three active valves.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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