# Homework Help: Need Help Setting up Differential Equation

1. Sep 9, 2008

### swooshfactory

1. The problem statement, all variables and given/known data

A tank contains 3200 L of pure water. A solution that contains 0.11 kg of contaminent per liter enters the tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate.

with C representing the amount of contaminent in kg at time t (in minutes), write a differential equation that models this situation.

2. Relevant equations

possibly int(udv) = uv - int (vdu) (integration by parts)

3. The attempt at a solution

rate in: 8 L /min * .11kg/ L = .88 kg/min I am confused about where to put the variable t here. From my solution, it would appear that .88/t would be right, but then the rate in would decrease over time. This doesn't seem right. Would it be .88t or .88/t or just .88?

rate out: 8 L/min * C(t)/3200L = C(t)/400 kg/min.

DC/dt= rate in - rate out

DC/dt= .88t - C(t)/400

Is this correct? Should I have added the "t" when it is kg/min?

***In my most recent attempt at this problem, I have come up with:
dC/dT = .88 - C(t)/400

Last edited: Sep 9, 2008
2. Sep 9, 2008

### Dick

dC(t)/dt=.88-C(t)/400 is correct.