Hi Carol,
I'm pretty sure that it has to do with density, and which thing (water, salt water, egg) is more dense. Check out this activity, which explains this very principle:
http://www.education.com/magazine/article/teach_density_fourth/
An egg will sink in normal tap water. This is because eggs have a higher density than tap water. Density is the ratio of the amount of matter in an object compared to its volume. That is to say that a small, heavy object, such as a rock or a lump of lead, is denser than a larger object of the same mass, such as a piece of cork or foam. Essentially it means an egg weighs more than an egg-sized amount of tap water. In the same way, a nail is heavier than a wooden stick of the same size because steel is denser than wood.
Salt water is denser than an egg. The egg weighs less than an egg-sized amount of of saltwater. Because of this, an egg is similar to a helium balloon in the air. The balloon’s density is less than the surrounding air and therefore it floats. Likewise an egg floats in saltwater.
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