Modeling differential equations (2nd order?)

Demerdar

Here's my problem:

A tank with a capacity of 3000 liters contains 1200 liters of water with 8 kilograms of
dissolved salt. A solution of salt and water with a concentration of 25 grams of salt
per liter of water flows into the tank at a rate of 10 liters per minute. The well mixed
solution flows out of the tank at a rate of 7 liters per minute. Find the concentration
of the mixture in the tank at the instant it begins to overflow. Set up an initial
value problem, solve it, and complete the analysis to answer the question posed in the
problem.

I know how to solve these when the water level remains constant, but when it is constantly increasing, I'm not sure how to model it. If the tank's inflow equaled the outflow, the differential equation is first order (ie)

dQ/dt = inflow-outflow (quantity/unit time)

However, since the tank is continuously filling up, I'm not quite sure how to set up this differential equation. The professor hasn't discussed this in class and I don't have a book at my disposal until tomorrow. So, any help would be generally appreciated. I'm not asking you to answer this question for me, I just need a little guidance.

BlazeFire

It's late and I don't have paper to work it out, but it should work out the same way. Since it is continuously filling, that just gives you information to know at what time you want the concentration at.

You start at 1200 litres, you gain 3L/min. You have 1800L to go... so it would take 600min.

dQ/dt = inflow - outflow as usual, so solve the differential as you normally would, then find out what Q(t=600min) is.

Demerdar

thanks, sounds right. overthunk it i guess.