MIAMI — Seven people, including a 4-year-old girl, survived 20 hours at sea by clinging to their capsized boat and a small blue cooler after their vessel flipped during a fishing trip off the Florida Keys, officials said today.

An 80-year-old woman who was with the group is missing and presumed drowned.

Three other women on board told rescuers they didn’t have time to grab life jackets for anyone except the girl when two waves suddenly flipped the boat off Long Key in choppy, rainy waters Saturday afternoon, Seaman Kendra Graves said.

Three men on board tried to help the 80-year-old woman, but she went under the water within minutes of the 22-foot-long boat capsizing, said Florida Fish and Wildlife Spokesman Robert Dube.

“She was one of men’s mother — he could not hold onto his mother and she went under,” Dube said day.

At some point, the boaters drifted apart — three women and the girl hanging on to the cooler; three men holding on to the boat.

A commercial fisherman spotted the capsized boat Sunday morning, Dube said, and rescued the men clinging to its bow. The women and girl were soon picked up by the Coast Guard, several miles from where the boat had capsized.