I live in a modern flat that seems to have one main outlet for waste for the whole flat. My kitchen sink is OK but my bath water is very slow to empty. I have just purchased a washing mackine and plumbed it in under the kitchen sink. What is happening is the water from the washing machine emptys into the u-bend which then fills and backs up into the pipe and back into the sink. This then has the problem of the dirty washing water going back into the washing machine and dirtying the clean wash. Any ideas please

Bath drains clog with hair. Try drain cleaner products first. Keep trying until it drains quickly. And buy a hair trap, a plastic one that sits on top of the drain.

You should not plumb a washing machine into your kitchen sink drain (unless you are in a country where 'washing machine' means what is called dishwasher in the US)? But you say it dirties the wash... a washer needs it's own open top 2" drain pipe several inches above the top of the washer, with the flexible drain hose loosely put in the opening at the top. The reason is the force and high volume during the drain cycle needs a lot of room, and the height is required to keep it from backing up.

Try drain cleaner products first. Keep trying until it drains quickly.
I disagree! I am no fan of putting harsh chemicals in your system. Besides, they only seem to work in TV ads and a person could damage their eyes if they attempted to snake a line full of lye water.
A safer way and one more likely to clear your blockage would be to remove the "J" band and send a snake up into the wall, You'll hit a bend about 8 inches in but once past that you only have 6 more feet to go.

You should not plumb a washing machine into your kitchen sink drain
Again. I disagree! In a septic tank system both the kitchen and washer are combined to go through a grease trap before going to the septic tank. And in regular city sewer the kitchen and washer are usually on the same wall so they are combined also. Some codes now mandate a 3" drain line for both. REgards, Tom

Tom, I defer to you about the way to plumb (and the OP changed her or his question a lot since I replied). But I have safely used both liquid drain cleaners and lye crystals in tubs that had no access or no easy access. Probably 15 times in 45 years.

Tom, I defer to you about the way to plumb (and the OP changed her or his question a lot since I replied). But I have safely used both liquid drain cleaners and lye crystals in tubs that had no access or no easy access. Probably 15 times in 45 years.
And you lucked out. I know of a case where a plumber was blinded when he remover a "P" trap full of draino, (lye) and it splashed in his eyes. Your eyes-your choice. Tom

I assume you live in the States...

Two things are happening with your installation:

1. Sink drain is too small
2. Sink drain is partially clogged

Washing machines require 2" drain and trap with 30" stand pipe. Also, kitchens sink drains are known to be the most "dirty" drains in your house reducing size of the pipe. Volume of water being discharged from washing machine is too high for this drain to accept. See if you can connect it someplace else.

Back to you. Milo