# Homework help with mixture problem

1. Nov 20, 2004

### Deanna

I need help setting this problem up. I keep coming up with the wrong answer. I know it is suppose to be either a separable or linear differential equation. Can anyone help me get it set up right? I think its suppose to be a linear 1st order diff equation.

A 100 gallon tank is filled with pure water. At time t=0 a salt solution is added to the container at a rate of 1 gallon per min. The well stirred solution drains from the container at the same rate--1 gallon per min. The concentration of the salt entering the tank is unknown. After 100 minutes it is measured that the amount of salt in the tank is 50 pounds. Determine the concentration of the salt (in pounds per gallon) in the incoming solution.

This is what I do know.
t(0)=0
t(100)=50
dV/dt=rate solution enters the tank - rate solution leaves the tank so
dV/dt=0
so v(t)=0+C and I believe C should = 100 which makes v(t)=100
I am not sure if this is right and I can figure out how to get dx/dt or where t fits into the equation. Help please if you can

Last edited: Nov 20, 2004
2. Nov 20, 2004

### Tide

The concentration in the tank is governed by

$$\frac {dC}{dt} = (C_{in} - C) \frac {R_{in}}{V}$$

where $C_{in}$ is the concentration of the solution flowing into the tank, $R_{in}$ is the rate at which the solution flows in and V is the volume of solution in the tank. You should be able to take it from there.