# Mixing problems using DE's

I am having major problems understanding these types of questions, where you will have water and in will be chemicals mixing at a certain rate, and coming out of another tube at a rate, and then the question is to find out certain things, concentration at a time or whatever.

My question, the equation takes the form

dx/dt = in - out

x is the amount of chemical

The in is the rate coming in, however it seems the out part is usually the number multiplied by some other stuff. The question is, how do I know what to put in ''the other stuff''?

miglo
the other stuff will be A/V where A is the amount of chemical and V is the volume of water in the tank
when setting up the differential equation you leave A alone since that is what were trying to solve for
for V, you take initial amount of volume+(rate in-rate out)*t
where rate in and rate out are in liters/min or whatever units you are using

how about when a chemical and water mix is already in the tank, and you are now pouring in pure water? How do I express that?

how about when a chemical and water mix is already in the tank, and you are now pouring in pure water? How do I express that?

Then if your rate of change depends on that it will be some function of what's already in the tank which is some function of x.

$$\frac{dA}{dt}= -Ar/V$$.