Police say that a month after vanishing without a trace, a Minnesota teen has been reunited with her family following her escape from captivity

Police say that a month after vanishing, a Minnesota teen has been reunited with her family following her escape from the three men who had allegedly held her captive, PEOPLE confirms.

According to investigators, all three men are suspected of sexually assaulting the 15-year-old girl, who was last seen on Aug. 8 leaving her home in Alexandria, Minnesota.

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Alexandria police said in a statement that the teen was found on Tuesday running through a field in adjoining Grant County, Minnesota. She happened upon a stranger and told them who she was and asked that they call 911.

According to police, the girl told them she had been abducted several weeks earlier, and then she led detectives to the men who were allegedly responsible: Thomas Barker, 32, Steven Powers, 20, and 31-year-old Joshua Holby.

All three have been arrested and charged with kidnapping, false imprisonment and assault. They are held without bail. They have not yet entered pleas or retained attorneys who could comment on their behalf.

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Police said in their statement that, according to a preliminary investigation, the teen was approached by Barker, whom she knew, outside her home around 11 p.m. on Aug. 8 “on the pretense that he needed help with a situation.”

“She offered to assist and entered Barker’s vehicle,” police said.

At that point, Barker allegedly drove her to his home, where “he restrained her with zip ties, repeatedly assaulted her and threatened her with weapons,” police claim.

Barker and Holby are roommates, according to investigators, who suspect Holby also “took part in the assaults, as did Mr. Powers, who arrived at the home about [two] weeks following the abduction.”

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The assaults happened regularly over the last few weeks, police allege. The girl was also recently taken from the home to “various locations including a cornfield and a foreclosed property in Grant County,” police said.

And then on Tuesday, for “the first time in 29 days, she was left alone.”

She fled to several nearby homes, seeking aid, apparently without success, before swimming across part of Thompson Lake to locate a residence where someone could assist her, police said.

Authorities believe the girl was both physically assaulted and sexually assaulted, and she spent much of her captivity locked in a closet.

She told police her kidnappers did feed her, bringing her fast food meals to subsist on.

The girl’s family has requested privacy, according to the Minneapolis Star Tribune. But her mother did reportedly post a photo on social media of the two reunited on Tuesday night, with the girl smiling and her hair still wet.