Chapter 3.4, Problem 43ES

The thin lens equation in physics is

$\frac{1}{s}+\frac{1}{S}=\frac{1}{f}$

Where $s$ is the object distance from the lens, $S$ is the image distance from the lens, and $f$ is the focal length of the lens. Suppose that a certain lens has a focal length of $6\text{ cm}$ and that an object is moving toward the lens at the rate of $2\text{ cm/s}$ . How fast is the image distance changing at the instant when the object is $10\text{ cm}$ from the lens? Is the image moving away from the lens or toward the lens?