Snakes are cheap and can solve a lot of problems if they're minor. I'd start there. If that doesn't do it, I'd spend a few bucks on a commercial routing service.

Good news is that it's probably a one-time thing. Once you've got them running freely again, I'll bet that'll be it.

Ah, the joys of older homes! Hope there's no gremlins in there.

I found a ton of grout in a not-so-old home with a slow shower, I did my landlord a big favour and cleaned it out of the trap myself...what a difference! I may have saved them the problem of a leaky recess too, since the water then no longer pooled in the shower.

As far as I could tell, the grout really only collected in the trap, are you sure the grout extends into the drain as well? It's soft stuff, so snaking might help. I just saw that Rigid tools make a mini, retail-type drain type camera (only a short reach though) you might be able to rent one also, just to look a bit further up there. A mechanic's dental mirror and a decent light might help too.

Most drain cleaners are caustic but if there's one that's acidic and suitable for your types of drain, you might be able to dissolve it slowly chemically as well. I'm not sure how even vinegar would work, but it wouldn't harm the drain or the environment in reasonable quantities.

Solved one of the two slow drains tonight after work. I bought a snake, took the P trap out of the tub. I didn't find a visible obstruction, but once I got done snaking the two lines which the tub drain go into (Tee). The tub drains fine. The sink on the other hand is still slow. I thought maybe the sink and the tub both t-d into the same drain line so I had snaked the sink line. Apparently that's not the case. Tomorrow if I feel up to being covered in junk I'll snake the sink....

Snaked the sink drain tonight. Pulled out some hair and other gunk. So far I'm two for two. Thanks for all the advice.

-Gil