Peel, core, and slice apples, and then slice carrots. Add both to a large pot and pour water over top. Bring to a boil and then cover and reduce to a simmer. Simmer for about an hour, stirring occasionally, until carrots and apples are soft. Remove from heat and allow it to cool until just warm. Transfer to a blender or food processor and blend until smooth. If mixture is too thick, add a tablespoon of water at a time until desired consistency is reached. Makes about 1 quart. Store in refrigerator for up to a week.