Police and fire personnel are assisting in his search, the department said. Javier Cantellops, one of the rescuers who found Amanda Eller on Friday, said during a news conference over the weekend that he was meeting with Mina's family to put together a search team.
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"Circumstances are completely different ... but overall it's the next mission," he said at the Saturday press conference. "He's another member of our community."
Mina's father, Vincent Mina, said in a Facebook post that Noah has been missing since last Monday when he went for a hike that morning and hopes his son's story ends as Eller's did, with his safe return.
Mina is described as 5-foot-8, 180 pounds, with shaven black hair and brown eyes.
Eller, 35, was discovered by a helicopter crew on Friday, after going for what was supposed to be a short hike on May 8. She was reported missing by her boyfriend, Benjamin Konkol, the next day.
Authorities said Eller left her SUV, with her wallet and phone inside, at the Maui reserve before going on her trek. Her mother, Julia Eller, said at a news conference on Saturday that her daughter intended to go on a 3-mile hike but became disoriented after stopping to rest.
Eller tried to follow her instincts to get back to her car but "was going in the wrong direction," her mother said.