Slow bathtub drains are often caused by an accumulation of hair, soap scum, and little bits of debris that get caught up in the first part of the drain assembly.
Unless your home is really old and hasn’t been updated, your bathtub drain assembly will look something like this with a drain at the bottom of the tub with an overflow and both of those come together and flow into a p trap and after that flows into the rest of your home’s drainage system.
What happens a lot of times is that at the bottom of the drain, there’s a cross-section, and hair gets caught up on that and collects over time. This is one of the most common blockages especially if your tub has a shower attached to it.
