Originally Posted by

**DMDil** Consider the two interconnected tanks as shown below. Tank 1 initially contains 30 gal of water and 55 oz of salt and Tank 2 initially contains 20 gal of water and 26 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min. The mixture flows from Tank 1 to Tank 2 at a rate of 3 gal/min. Water containing 3 oz/gal of salt also flows into Tank 2 at a rate of 1 gal/min (from outside). The mixture drains from Tank 2 at a rate of 4 gal/min, of which some flows back into Tank 1 at a rate of 1.5 gal/min, while the remainder leaves the system. Let us denote by

Q (t) and Q2(t) the amount of salt in Tank 1 and Tank 2, respectively.

how to

Formulate a system of differential equations for

Q1(t) and Q2(t) and initial conditions that describes this flow process.

i know how to solve this, but don't know how to set it up equation of Q1, Q2..

I will do the equation for $\displaystyle Q_1$ and leave the other for you. For tank 1

Inflow: $\displaystyle 1.5 +\frac{1.5}{20}Q_2(t)$ oz/min

Outflow: $\displaystyle \frac{3}{30}Q_1(t)$ oz/min

So using minutes as units of time we have:

$\displaystyle

\frac{dQ_1}{dt}=1.5 +\frac{1.5}{20}Q_2(t)-\frac{3}{30}Q_1(t)$

CB