My solution is... Tolkien was above such mundane things.
When I was... 5? 6? ans my mother read LOTR to me, one of the main questions that bothered me was how come the book follows the life of the Fellowship for days on end and it doesn't say that they went to the bathroom or took a nap or had a snack even once! Did they walk non-stop for all thoe days without going to the bathroom?! ...This always made me laugh ever since I "got" it. And your question made me think of that.