Cook the ground beef in a skillet over high heat until crumbly and browned. Pour off as mush grease as you can, then stir in the soup, water, ketchup, and Worcestershire sauce.
Bring to a boil, then stir in the potatoes. Reduce heat to a simmer, cover, and cook 10 minutes. When the potatoes are tender, place the American cheese on the potatoes, cover, and cook another minute until the cheese melts.