Just moved into this older house 3 weeks ago. Drains were initially a bit slow, but no real drainage problems other than the kitchen sink gurgled when the washing machine drained. Yesterday drains starting backing up, sinks, shower, toilet etc. The water will drain after it backs up, usually takes about 20 minutes, but will back up again when water is run for the length of an average shower. I was originally thinking the vent may be obstructed and was planning to get up on the roof to check those and snake them or run a hose down them. Now that it is back up I am a bit more nervous about a possible bigger problem. I was thinking about locating the main clean out tonight and trying to snake it or flush it out with a water dam hose attachment. Hoping there is not a problem with the main line that feeds to the city sewer. Am I wasting my time, should I just call a plumber? I just bouoght the house and money right now is tight to say the least. Thanks in advance for any advice.

You have several issues going here.
the kitchen sink gurgled when the washing machine drained The kitchen vent's blocked. Snake from the roof. Put out enough snake to reach the base and 15 more feet.
You also have a partial blockage blockage in your drainage but before it can be snaked it must be located. Locate the house cleanout and open it up. Give it a couple of flushes. If water backs up in the cleanout the blockage's is between the house and the street, If it's not backing up then the stoppage is in your house, Good luck, Tom