Question

A tank contains 1000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept throughly mixed and drains from the tank at a rate of 15 L/min. Determine the amount of salt in the tank after t minutes.

Answer 1

Here is a similar example and I think it will help you solve it.

Answer 2

I know the general setup for these types of problems is
\[\frac{dx}{dt}=\text{(rate in)(concentration in)} - \text{(rate out)(concentration out)},\]
but the second and third sentences are throwing me off. I think the (rate in)(concentration in) term is
\[\left[\left(0.05\frac{kg}{L}\right)\left(5\frac{L}{min}\right)+\left(0.04\frac{kg}{L}\right)\left(10\frac{L}{min}\right)\right],\]
but I'm not absolutely sure.

Answer 3

If my first impression is right, then the differential equation for this problem is
\[\frac{dx}{dt}=0.65-\frac{15}{1000}x(t),\]
which is fairly easy to solve once you find the integrating factor.

Answer 4

that is correct @SithsAndGiggles we did one that was somewhat like this and that is one of the notes that i have here

Answer 5

that sounds right to me

Answer 6

Alright then! Do you need help solving it?