In a large saucepan over high heat, combine carrots, potatoes and enough water to cover by 1 inch. Bring to a boil. Reduce heat to medium. cover and cook 15 to 20 minutes, or until vegetables are tender. Drain.
In a 2 1/2 quart baking dish, layer carrot slices to cover bottom. Sprinkle 1/3 brown sugar, salt and pepper on top and dot with 1 tablespoon margarine. Continue layering until all ingredients are used up, sprinkling each layer and brown sugar and dotting with margarine. pour 1 cup water over mixture.
Cover and bake 30 minutes until apples are tender. Uncover and bake 5 more minutes until top is golden.