# Mixture problem. How to solve for C?

by Jeff12341234
Tags: mixture, solve
 Sci Advisor HW Helper Thanks ∞ PF Gold P: 5,043 Mixture problem. How to solve for C? OK. I see what you did, and, of course, it is right. But, here's my alternate version to consider: $$\frac{dV}{dt}=f_{in}-f_{out}$$ $$\frac{d(VC)}{dt}=f_{in}C_{in}-f_{out}C$$ Multiply the first equation by C and subtract it from the second equation: $$V\frac{dC}{dt}=f_{in}(C_{in}-C)$$ where $V=V_0+(f_{in}-f_{out})t$ So, $$\frac{dC}{(C_{in}-C)}=f_{in}\frac{dt}{V_0+(f_{in}-f_{out})t}$$