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Water heats faster when it is covered, partly due to the second law of thermodynamics. The law basically says that heat always flows toward cold. The air above the pot of water would be at room temperature, though it does gradually warm up as the water is heating. This means that as the water is being heated to 212 F or 100 C, some of the heat is escaping to heat the air that is in contact with the water.
When you put a lid on the pot, the air is contained, so it takes less time for the temperature to reach the boiling point.
However, the difference in time isn’t very big. Air gains and loses heat much faster than water does. Thus, the amount of heat that is lost to the air isn’t very large. For that matter, the pot is also losing heat to the air for the same reason, yet the pot remains too hot to touch when the heat and the contents are removed because the heat doesn’t immediately flow into the air, despite the much larger volume of air that the heat is able to flow into.