Modelling Salt and Water Flow in a Tank

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A differential equation is established to model the flow of salt and water in a tank, where 2 tons of salt enter a 20-ton tank of water each minute, while 2 tons of the mixture are drained simultaneously. The equation is represented as \frac {d}{dt} \frac {S^2 + W^2}{S+W} = \dot S, with W(t) indicating the water amount and S representing the salt amount, calculated as S = S_0 + \dot S \times t. The discussion also touches on uncertainty regarding the setup, with participants questioning the validity of their approaches. Clarification on the modeling process is sought, emphasizing the importance of accurate representation in differential equations. Overall, the conversation highlights the complexities involved in modeling fluid dynamics in a tank system.
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set up a differential equation to represent 2 tons of salt entering a 20 ton tank of water each minute while 2 tons of the mixture are drained each minute
 
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\frac {d}{dt} \frac {S^2 + W^2}{S+W} = \dot S

where W(t) is the amount of water in the tank and S is the amount of salt given by S = S_0 + \dot S \times t with \dot S being the constant rate at which salt is added.
 
Are you sure about that tide? I could swear I tried that same thing, but I don't know, maybe I was just being an idiot. Thanks for the help
 

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