Just a point to those who are saying if they had shared the board that would have both lived, that they were stupid and stuff like that because they didn't share the board, if you were in 28 degrees farenhite water and dying of hypothermia plus cold, wet, in great pain and practically dead would you be able to think straight enough to share the board. Also, another point, that when they first got in the water and were getting on the headboard he tried to get on but it almost flipped back on top of them. Plus it was already slightly under water with her on it(if only a couple centimeters at the most). With both of them I think it would not have stayed a float. Even more so, Jack says that when you're in the water you can't think of anything but the pain at the beginning of the movie, I wouldn't be surprised if they couldn't think of anything of pain and Jack only thinking of saving her. She had never been in that kind of condition before, when you're not expecting that type of pain it hits even harder and you can barely think.(Speaking from experience here.) Just my opinion of course though.

::EDIT:: P.S. I know that they didn't really exist.

Also, from what I've looked up, there was a Jack(Joseph) Dawson on the ship, he was a cook.