yes, you could replace the pipe but before doing that, I'd give thought to the pipe being partially blocked, causing the water to back up. If you can, trace the pipe back to where it dumps into the main sewer, look for a clean out and take a look. built in 69' is a "newer" house.
The drain pipe must be at least 2 inches in diameter and the open end must be at least 18 inches above the trap. If not then it likely that a modern washing machine will cause it to overflow.
(One morning on WRKO Radio) The tub's not clean! Let's remodel the bathroom.
(One afternoon on WRKO Radio) It's time for an oil change. I'm going to trade in the car for next year's model.