It is "tract." Nice catch.
It's not just Middlearth, either. I mean, did you read about Sydney Carton asking to use the gaol bathroom before they cart him off to the guillotine? He was there for two days! And in her ten years at Lowood, did we ever read about Jane Eyre running off to the privy?
In general, authors avoid writing about bathroom functions unless it's an essential part of the story: as in, writing about someone with Crohn's disease, or making a point about the horrible food at someone's house. It saves time and awkwardness.
P.S. (I know the thread is a joke. Viva la digestion-less hobbits!

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