#### kankerfist

##### New member

- Joined
- Mar 22, 2006

- Messages
- 22

5 lb of salt is initiall dissolved in a tank holding 15 gal of water. Saltwater is pumped into the tank at a rate of 2gal/min and the fully-mixed solution flows out of the tank at a rate of 3 gal/min. If the salt concentration entering the tank is 2lb/gal, determine the amount of salt in the tank at time t.

I built the following differential equation in order to find the amount of salt at time t. I'm not sure if I set this part up correctly:

\(\displaystyle \left\{ \begin{array}{l}

S'(t) = 4 - 3\left( {\frac{{S(t)}}{{15 - t}}} \right) \\

S(0) = 5 \\

\end{array} \right.\)

where S(t) is lb of dissolved salt at time t. When I solve this initial-value D.E, I get the following solution for S(t):

\(\displaystyle S(t) = - 2(t - 15) - \frac{{25\left( {15} \right)^3 }}{{(15 - t)^3 }}\)

But my teacher's solution is:

\(\displaystyle S(t) = - 2(t - 15) - 25\left( {\frac{{15 - t}}{{15}}} \right)^3\)

I think my problem is that I did not make a correct differential equation that reflects the system. Any help would be appreciated!