What is the Formula for Dilution with a Full Tank and Only Fresh Water Inflow?

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Homework Help Overview

The discussion revolves around a dilution problem involving a tank filled with saltwater and the inflow of fresh water. Participants are exploring the implications of the rates of inflow and outflow on the concentration of salt over time.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are examining the relationship between the rate of salt inflow and the concentration of salt in the tank, questioning whether the rate in should be considered zero when only fresh water is added.

Discussion Status

The discussion is focused on clarifying the definitions of variables and the conditions under which the rate of salt inflow is considered. Some guidance has been provided regarding the interpretation of the variables involved.

Contextual Notes

There is an ongoing examination of what the variable y represents in the context of the problem, specifically whether it refers to the amount of salt or its concentration, which influences the understanding of the rates involved.

neshepard
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I have a problem I finally answered, but it made me think. The formula is dy/dt=rate in - rate out for dilution. If a tank is full of salt and only fresh water flows in, are we treating rate in as 0 if we are looking to find how much salt is left at any time t?
 
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It depends on what y represents. If y is the amount of salt or concentration of salt at time t, then yes, the rate in is zero.
 
Yes, y represents the amount of salt and t is the time. So the only time there is a rate in for the formula is if there is actually, in this case salt, flowing in?
 

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