Given that and decreases at a rate of , find the rate of change of when and .

Given that $\frac{1}{y} + \frac{1}{x} = \frac{1}{12}$ and $y$ decreases at a rate of $1\text{ cm s}^{-1}$, find the rate of change of $x$ when $x = 5\text{ cm}$ and $y = 1\text{ cm}$.