lots of water dumped ikitchen sink overwhelms drain and backs into clothes washer box

Hi- We are looking at purchasing a 1964 home with lots of "renovations" over the years. The disclosure says that if you dump a very large amount of water in the kitchen sink (5 gallons), it can overflow the clothes washer wall box below... I think they added the laundry below in the most recent remodeling,of the basement, and tied the washer box's drain line into the sinks drain line coming down in the wall from above. Any ideas? Run from this house or is this an easy fix, or live with it and just be careful?
Thanks,
RT

Anything can be fixed, but without seeing what is causing the problem we would be stabbing in the dark as to what it would take to correct it.
You would be better off placing a dollar value on the problem. If it will cost $500 to fix, would it stop you from buying the house? How about $1000? $2000?
Point being, everything has value, and every house needs something fixed. The numbers you attach to it are up to you.

WE do not know WHY the water overflows or how it was installed so we have absolutely no idea what it would take to fix it. It might just require a drain cleaning that the previous owners did not want to pay for as long as they could get by with just draining the water slower.