The cage that held Naomi was farther than what he saw from outside the water. It took him more than ten seconds to reach the cage.
Naomi was very glad to see Jack. She wanted to say something but couldn't. The cage was not the fully closed type. The inside was filled with water as well.
Since they couldn't do messages, Jack tried reassuring her using his version of sign language. Dina didn't understand then, and Naomi also didn't. She just nodded repeatedly to express her gratitude.
Jack swam around the cage and saw a keyhole at one of the cage's sides.
'A keyhole… means there is supposed to be a key somewhere,' Jack thought.
He looked around. The key must be in this pool. There was nothing outside unless it was at the bottom of the ice box under all those meats.