really really off the wall question about plumbing,,i need the true pro's here,,,, drain backing up?

house about 60 years old,,original pipes go from kit sink,,dw,,to bath then out east to yard,,angle to corner of lot 15 years back ,,addition to house ,,utility room,,bath,,out north to yard,,to corner of lot,, lines tie here and to city sewer,,which I am told is a 3 " pvc inside a 4" tile (is this possible) when dw and washing machine both running,,water backs up in original tub,,but not in added tub,,(both on same level) have been told this was a vent issue any other ideas?? here is where the pro comes in----can i talk into the bath overflow and hear it on the roof if I can get water out of trap?? hey its Saturday and what else do you have to do huh,,,taxes