I recently purchased a new house, and am renting to people downstairs.
I have a washer that is connected to my sink that I use from time to time.

Today, the tenant informed me that the sink and washing machine was overfilling with MY laundry water. I'm not very good with plumbing, but there are several facts that I am aware of.

1. The overfill problem usually only occurs when I use my washing machine.
2. When the house was up for sale (noone else using water), the tenant had no problems whatsoever.
3. The water has filled up the tenant's sink, and over. Also, the water gets backed up through her washing machine, and inside it.
4. Based on 1-3, I assume they share the same pipe.
5. The house is really old. (Built around 1920)

What can I do to stop the overflow problem?

I can take pictures if needed.