When a 24-year-old woman answered, Smith allegedly introduced himself as "David" and tried unsuccessfully to sell her a magazine subscription.
After the woman said she wasn't interested, Smith told her he was thirsty and asked for a drink of water. When the woman turned around to get the water, she later told investigators, Smith walked into her home uninvited, Roderick said.
At some point, the woman apparently decided to make a purchase and went to her bedroom to get her wallet. Smith followed her in, overpowered her and then raped her, Roderick said.
Layton detectives tracked the traveling group of magazine sales people to Logan and determined that a "David," who matched the description of the man they were looking for, had been selling items in Layton on the day of the alleged rape.
They took him into custody on Friday and interviewed him.
Smith allegedly told officers that he did have sex with the woman, but it was consensual, Roderick said.