You guys are overthinking it.
Train stations. Seriously. You hop on them to go to work, along with rush hour people that head to the nearest industrial center. Other ties they head home. Even though there will be as many west bound as east bound the time of day is different. Since it's a Saturday and he doesn't work chances are he's leaving at the somewhere near the same time and will always end up either on the homeward bound train or the workbound train.