My tubs are backing up only when my washing machine drains. I thought it was my sewer line and used an auger to clear that, but it's still happening. Could I need a new washer? This one is over 10 years old.

You may need to check the exhaust lines that run to the roof. In order for the water/soap residue to flow easily out to the sewer, it needs to have good access to open air, or you get the same effect in your drains as you do when turning a soda bottle completely upside down. The "glug" effect.

Mine was doing the same thing, and my access pipe actually wasn't opened right. Guy came out and ran a 20 foot pole up and down through it, charged me $20, and no problems since!

While this could be a blocked vent my bet's on a partial blockage in the washer drain line. The reason you see it with the washer is that the washer pump discharges with more force and pressure then any other fixture in your house. Snake the washer line from the washer roof vent and be sure. Put out enough cable to reach the base and 20 feet more. Test by cycling the washer. Good luck, Tom