Judging by his better looking image from BioShock 1 here he looks like he's suppose to be around the 19-25 age mark. Though the old looks could be contributed to the amount of ADAM he used, the effects of his rapid experimental growth by Suchong & Tenenbaum or just Irrational Games going "Ah why the hell not let's just make Jack look very old
And lastly, how they forcefully tied the bioshock universe together just felt like they tarnished bioshock 1's perfect storyline for no good reason. It felt rushed, completetly forced, and just plain silly. I keep seeing this DLC get praised, but I really really can't handle plotholes like this.
Burial At Sea is an overt claim of ownership over both BioShock fictions - Rapture's city beneath the sea and Columbia's city above the clouds. Clearly I won't go into detail as once the spoiler avalanche starts I don't know that I could stop it, but this goes further than before in terms of inextricably linking the two worlds.
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bioshock burial at sea explained