Press ups hands close together and far apart work not only the arms and chest but the back...also if the other half has some dumbells or barbells then you're made...exercises for the lats would be dumbell pullovers, upright row with resistance bands, bent over rows with barbells or dumbells...or you could do the callanetic arm thing...you can also do the pullups or chin ups on a door frame (I have one of those bars you can buy to put across the hallway up high)