It's actually my friend who is having the problem. She's only been living in the house for a few months, it was built in the early to mid 50's, and the drainage is with city sewer lines. Her washer and dryer are in her kitchen (common in these parts) next to her kitchen sink, and she told me today that her kitchen sink is backing up into her washing machine. To me it sounds like the first thing to would be to snake the line. I'm hesitant to tell her to use drano or another type of declogger, because they can be so hard on those old galvanized pipes. Any other ideas?

If the washer's connected to the kitchen sink drain then the sink line's clogged and must be snaked, Remove the bend from the trap and send a snake up through the wall. Put out about 7 feet of snake. Flush with hot water.
Good luck, Tom