Salt melts ice essentially because adding salt lowers the freezing point of the water. How does this melt ice? Well, it doesn't, unless there is a little water available with the ice. The good news is you don't need a pool of water to achieve the effect. Ice typically is coated with a thin film of liquid water, which is all it takes.
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Keywords: freezing point of water, colligative properties, ice, salt, freezing point depression