In a medium pot, combine the rhubarb, strawberries, and 2 1/2 quarts of the water and bring to a boil over medium-high heat. Lower the heat to medium and cook, keeping the mixture just below a boil and stirring occasionally, until the rhubarb and strawberries are very soft, about 15 minutes. Add the sugar, mix well with a spoon, and continue cooking until the sugar dissolves, about 1 minute longer.
Meanwhile, in a small bowl, mix together the cornstarch and the remaining 1/2 cup water to make a slurry. Using a large whisk, stir the slurry into the rhubarb-strawberry mixture and continue to cook until the mixture thickens slightly, about 5 minutes longer. Remove from the heat and let cool to room temperature.
Serve the drink chilled or at room temperature with long dessert spoons for eating the rhubarb and berries. It will keep in an airtight container in the refrigerator for up to 5 days.
