An industrial process contains the following step: An industrial process contains the following step:
An upstream process dumps dirty water into the upper reservoir where it slowly drips through the filter, collecting in the lower reservoir. After the upper reservoir is completely empty, the lower reservoir is momentarily removed and poured into a downstream process. An upstream process dumps dirty water into the upper reservoir where it slowly drips through the filter, collecting in the lower reservoir. After the upper reservoir is completely empty, the lower reservoir is momentarily removed and poured into a downstream process.
Occasionally, the upper reservoir is overfilled with dirty water. In these cases, the system eventually reaches the following equilibrium state: Occasionally, the upper reservoir is overfilled with dirty water. In these cases, the system eventually reaches the following equilibrium state:
Notice there is still an amount X of dirty water remaining in the upper reservoir. Notice there is still an amount X of dirty water remaining in the upper reservoir.
In this case, the lower reservoir cannot be removed because water will continue to filter through and drip on the equipment below. However, workers have devised an emergency solution: they manually siphon an appropriate amount of clean water out of the lower reservoir to make the necessary room. In this case, the lower reservoir cannot be removed because water will continue to filter through and drip on the equipment below. However, workers have devised an emergency solution: they manually siphon an appropriate amount of clean water out of the lower reservoir to make the necessary room.
Question: What is an "appropriate amount"? Is it amount X, or some other amount?
(More precisely: What is the minimum amount of clean water which must be removed from the lower reservoir in order to make enough room for all the dirty water in the upper reservoir to filter through, leaving the upper reservoir completely empty?)(More precisely: What is the minimum amount of clean water which must be removed from the lower reservoir in order to make enough room for all the dirty water in the upper reservoir to filter through, leaving the upper reservoir completely empty?)
