Melt 1/2 cup unsalted butter in a sauce pan. Stir in 3 tablespoons flour until smooth. Add 1/2 cup white sugar, 1/2 cup brown sugar and 1/4 cup water; bring to a boil then simmer gently for about 5 minutes.
Line a 9 inch pie pan with uncooked pastry crust. Fill crust with apple slices...(about 5 tart apples - cored and sliced) Put lattice crust on top. Pour the sugar and butter mixture over the crust. Bake 15 minutes at 425 degrees F (220 degrees C). Reduce the temperature to 350 degrees F (175 degrees C), and continue baking for 35 to 45 minutes.