Feasting on Food for Thought

Anyone who keeps a pet, or a few fish in a tank, has a halacha waiting at the table: a person may not eat before feeding his animals. So how did Rivka give Eliezer water before she gave his camels, when the Avos kept the whole Torah? The Gemara in Berachos learns the rule from the pasuk in Shema, and the Sefer Chasidim raises exactly this difficulty. Several answers follow, and some of them change how we should treat the animals in our care.