Somewhere, Steven Callahan is thinking, "About fucking time." Read this book last year - he really could have used that raft.
Less than a few days if you didn't have a good water source.
Given unlimited ketchup packets? Probably a long time. Assuming again a good water source.
Assuming you are not malnourished or lacking in vitamins, a few months minimum.
Edit - this guy did it with very little food 76 days. GREAT book, read it in 7th grade, maybe 20 years ago, I think this happened in roughly 1984. http://www.amazon.com/Adrift-Seventy-Six-Days-Lost/dp/0345410157
If you have a station that shows "I Shouldn't be Alive"... which shows on Discovery channel where I live... they did an hour long episode on this. Which pales in comparison to the 400ish page book where he enumerates his ordeal.
Edit 2 - It would be horrible for your health. Don't take some sort of foolish dare of your college buddies to prove it :)