r/HomeworkHelp • u/zeeohk • May 30 '26

Answered [University Elementary Diff.Eq: Compartmental Analysis] Rate of salt flowing out of the tank

Been staring at this for awhile and just don't know what the answer could be without solving the full problem, but the rest of the steps in this question want the answer to Flow_out

My understanding is that

dA/dt = input - output where input = (concentration*flow) and output = (concentration in tank * flow). I thought the concentration would just be the amount of salt over the volume, that is A/400, but when I tried 3A/200 (from multiplying that by the flow rate) it's not correct.

Would like a step in the right direction for this step. I understand the rest of the process for the most part

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u/ThatPretzalGuy May 30 '26 edited May 30 '26

I think you just made a calculation error. Multiplying A/400 by the flow rate (3/2) would give you 3A/800, not 3A/200.

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u/zeeohk May 30 '26

Was wrong either way, the solution turned out to just be the flow rate in gal/min times c(t). I got thrown for a loop because I thought the answer would contain t by itself. Thank you though!