Bring 4 cups of the water to a boil in a medium saucepan and add the tea bags. Remove the pan from the heat, cover it, and allow the tea bags to steep for
5 minutes.
Remove and discard the tea bags. Add the sugar to the saucepan and stir until dissolved. Add the remaining 3 cups water and stir to combine. Transfer the mixture to a pitcher, and add the lemon juice and rum. Chill thoroughly before serving.
Serve over ice, in tall glasses garnished with mint sprigs.
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