MARATHON, Fla. >> Four hours into a family fishing trip, rough waves flipped a 22-foot boat off the Florida Keys, tossing eight people overboard. Seven of them, including a 4-year-old girl, survived by clinging desperately to their capsized vessel and a small blue cooler for almost 20 hours, suffering exhaustion, jellyfish stings and hypothermia.

A 79-year-old woman, the matriarch of the group, was missing and presumed drowned.

"When the will to live kicks in, human beings can do amazing things," Coast Guard Petty Officer Nick Ameen said.

Those rescued were taken to a hospital with non-life-threatening injuries.

The family left Layton in the Middle Keys around 8 a.m. Saturday to go fishing in less-than-ideal conditions. It was raining, seas topped 7 feet and winds were whipping up to 38 mph. After they anchored 3½ miles off the island chain, two waves hit suddenly, capsizing the vessel.

The women grabbed the girl and the 2½-foot cooler. One of the men tried to rescue his mother, but she slipped through his grasp and disappeared into the water.

Almost immediately, the two groups — the three women and girl and three men — drifted apart.

Nearly a day later, they were rescued when a commercial fisherman spotted the men Sunday morning and alerted the Coast Guard, which found the women and the blue cooler several miles away in the warm waters.

The women said the boat turned over so quickly that there wasn’t time to grab life jackets for anyone except the child, said Kendra Graves, a seaman with the Coast Guard.

Florida law requires children 6 or under on a boat 26 feet or less to wear a life jacket if the boat is moving. If the craft is anchored or docked, they don’t have to wear a life vest.

As the weather improved Sunday, fishing boat captain David Jensen headed out with customers to catch live bait. Off in the distance, he saw a large object floating in the water.

As he turned the boat to get closer look, he saw a man waving. At first, he said, he thought there was only one person holding on to the sunken boat, its bow protruding just a few feet out of the water. When he got closer, he realized there were three men.

"I tried to get them to swim to the boat, but they said they didn’t know how to swim," Jensen said. "Then I had the mate throw them life jackets. One guy put on the life jacket and swam to the boat. The other two guys wouldn’t get off the boat. … They said they didn’t know how to swim."

One of Jensen’s customers jumped in and swam over. He tied the boats together, and helped the other two men, one at a time, back to Jensen’s boat.

"They were exhausted. One guy overnight had lost his mother," Jensen said. "He was very visibly upset, which was a little tough because he was the one who spoke the best English."

Zaida San Jurjo Gonzalez died. Her son, Jorge Alejo Gonzalez, survived along with his wife, Tomasa Torres, the elderly woman’s daughter, Elena G. Gonzalez, and her boyfriend, Juglar Riveras.

Also rescued were Jorge and Elena Gonzalez’s uncle, Jose Miguel De Armas, his wife, Yunisleidy Lima Tejada, and their 4-year-old daughter, Fabiana De Armas Lima. All are from South Florida.

After the men were found shortly before 9 a.m., the fishermen called the Coast Guard, who found the women. They started waving and yelling for help when they saw the Coast Guard vessel. They were hanging on to the floating cooler.

All of the boaters were soon reunited, wrapped in blankets and treated for shock and hypothermia.

"They were all pretty happy to see each other," Graves said.

It wasn’t clear if the boaters were aware of a small-craft advisory that had been posted early Saturday.

"They shouldn’t have been out there," said Florida Fish and Wildlife spokesman Robert Dube, whose agency is investigating. "It was nasty from the get-go."

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Kay reported from Miami.