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A saline solution contains $0.05\rm\,kg/liter $ salt. The saline solution flows into another tank with the speed of $3\rm\,liter/min$. What speed (in units $\rm kg/min$) is salt supplied to the tank?

My answer:

$+3\rm\frac{liter}{min} \times 0.05 \frac{kg}{liter}=0.15 \frac{kg}{min},~~v=?$

The salt is added to the tank with the speed of $0.15\rm\,kg/min$ - which is the correct answer.

But is there any way to describe this with a differential equation?

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    You're very welcome!2012-05-11

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An ordinary differential equation involves derivatives of a dependent variable (like $y$) with respect to an independent variable (like $x$). Here the two relevant variables are liters of salt in the tank and time. You know the rate of change of the first variable with respect to the second (indeed, it is a constant) so just set the derivative (of the first variable wrt the second, of course) equal to this known rate and you've written down a differential equation describing the situation.

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here the involved variables are linearly dependent...so while in calculation you are simply multiplying the rate,it is actually a multiplication by dy/dt...basically it is a very trivial kind of differential equation.you are forgeting that the rate you are talking about is basically a derivative...