Three factors that affect the rate at which ice melts are temperature, pressure, and the presence of impurities. Objects melt when they have reached an appropriate temperature and pressure where they can transition from their solid phase to their liquid phase. Impurities alter the temperature at which that happens.
All substances have a triple point, a specific temperature and a specific pressure where they can exist as a solid, liquid and gas all at once. If a substance such as ice is at a temperature at which is can transition from a solid, but the pressure is too low for it to become a liquid, it transitions directly into a vapor.
Raising the pressure on ice makes it melt at lower temperatures, while lessening the pressure makes it remain solid at higher temperatures. Impurities affect the melting point by making the liquid phase occur at lower temperatures. This is because the particles of the impurity are able to replace the small amount of the water present on the surface of ice. This displacement encourages the solidified ice to replace the water and melt. All impurities have this effect, but how much they change the melting point is determined by the size of the granules and their chemical properties.