Two capacitors, $C_1$ and $C_2$, are connected in series in an electrical circuit, forming an equivalent capacitance $C$, described by the following equation:
$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}$
If $C_1$ is increasing at a rate of $0.2\text{ F/sec}$ and $C_2$ is decreasing at a rate of $0.1\text{ F/sec}$, at what rate is $C$ changing when $C_1$ is $40\text{ F}$ and $C_2$ is $60\text{ F}$?