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By Alex Johnson and Elisha Fieldstadt

The families of two teenage boys who went missing while fishing off the coast of Florida pleaded for help Monday, asking people to scour the shores for debris or any clues that might lead to their sons.

The 19-foot white single-engine boat that Austin Stephanos and Perry Cohen, both 14, took out off the coast of Jupiter late last week was found Sunday, roughly 67 miles off the shore of Daytona Beach. There was no sign of the teens in the boat, according to the Coast Guard.

"We want everybody, once again, from Palm Beach all the way up the coast of Georgia ... to get on down there and look for anything off," Nick Korniloff, Perry's stepfather, said Monday.

Perry's mother, Pamela Cohen, asked that people specifically look for a Yamaha engine cover and a white YETI cooler that had been in the boat when the boys left — but which weren't discovered Sunday.

Capt. Mark Fedor, chief of response for the Coast Guard's Seventh District, said Monday afternoon that the removal of the engine cover "could indicate they were trying to work on the engine." But he said it remained unknown why the boat capsized.

Cohen told MSNBC that There were "multiple lifejackets on the boat [when it left, so it] was a very good sign that they only found one with the boat. We're all still completely faithful and hopeful that all these efforts will come with a positive result and bring our boys home to us."

Korniloff said his wife and Austin's mother, Carly Black, are distressed but determined to find their sons.

"My wife is a rock. My wife is strong," he said. "That woman wants her boy back, and Mrs. Black wants her boy back, and those women are not quitters."

The boys' families and football legend Joe Namath, who is a family friend, announced a $100,000 reward Sunday to anyone who helps lead to the teens' safe return.

"Our hopes are that they find those children," Namath said Monday. "There have been wonderful surviving stories of folks at sea."

Calling the search "an all-hands-on-deck-type effort," Fedor also said the mission was being carried out on the assumption that the boys are still alive.

"In warm water, you can survive for quite a few days — four to five days in these conditions," he said. But he said the open sea is "a challenging environment."

"This case certainly hits home," Fedor said. "I have a 13-year-old and a 14-year-old son at home, so this obviously resonates with me."

The Coast Guard expanded the search up to the waters off Jacksonville, about 270 miles north of Jupiter and 100 miles north of Daytona Beach. By the end of Monday, officials said, crews had flown 36 separate searches over three days covering more than 28,000 square nautical miles — roughly the size of West Virginia.