Originally Posted by kerry edwards

Most tub and sink drains eventually tie together so the problem is probably after they join. Go to Home Depot or Lowes and buy a good quality25' long 1/4 inch hand snake in a drum. (cheap ones are not worth it--they kink). I got a good quality Rigid snake at Home Depot. You'll need to remove the p trap from the sink to access the stub pipe coming out of the wall. You snake the tub down thru the overflow--you'll have to remove the face plate. Push the snake in, turning it if you hit a corner to get it around When the going gets hard and you feel the obstacle spin the drum and push it thru. 25' should get you being the 2' pipe into the 4' main drain which is probably clear. Pull out the snake. Immediately run hot water down the drains for at least 5 minutes. What often happens in situations like this is that on long runs with just a little drop, sludge will build up. It is black, slimy and virtually impossible to get off your hands. Wear latex gloves. This sludge can fall back into place once the snake has gone thru and resolidify. The hot water pushes it out. Have lots of paper or plastic around when you pull the snake out because there will be a lot of black sludge. Rinse off the snake.
Problem should be solved. Report back if not.
Remember the three rules of plumbing:
Get the stink above the roofline
Water flows downhill
Dont bite your fingernails

One warning. I once snaked out a poorly plumbed system. The snake went up the badly corroded galvanized vent pipe instead of the drain and became lodged in the rust. I had to take t he wall apart and remove the pipes to get the snake out. I now approach obstacles cautiously, snaking in an inch or two, then back out to avoid repeating my mistake.

By the way, a plugged vent can cause poor drainage. It is almost always accompanied by gurgling in the drain.