Clean water has very little extras in it so it takes the standard time to boil, versus other liquids like tea has larger percentage of alternate molecules which means it can heat up faster. Some other concentrations of different liquids can actually delay boiling, such as automotive coolant/antifreeze.
Time to boil is just heating power and time. There are two parts of this: the starting temperature of the tap water and the starting temperature of the equipment (stove, burner, kettle).
If your tap water is 40 degrees F/5C, then it needs to be heated by about 170 degrees the first time. But also everything else is starting at room temperature (70F/21C). So all of that needed to be heated first before the water temperature would increase.
But if your teapot *starts* warm, and the stove burner *starts* warm, more of that energy goes directly into the water, which can’t cool below room temp. So your tea was at least 35+ degrees F closer to boiling, and the equipment you used to boil it was also preheated, so it re-boils in less time.
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