Once the woman obliged, the man grabs her around the neck, punches her in the face several times, and violently grabs her off the bench. He drags her across the platform and throws her onto the track.
The 23-year-old victim was able to get up from the track before a train arrived and walk to the southbound track, where she climbed back onto the platform.
Meanwhile, the man walked out of the station with the victim's cellphone, police said.
Police said they do not have a motive.
Authorities said they chose not to announce the incident when it happened because they did not want to compromise the investigation by giving a description of the suspect's jacket.
"It was so distinct that we tried to keep the description of that jacket in law-enforcement circles, because it was our best lead on clearing this," Chief Thomas Nestel said during a news conference. "With our partners in the Philadelphia Police Department, we increased the number of officers out on the platform in our stations, and there were many people looking for this person."
SEPTA police arrested the man near 15th Street and John F. Kennedy Boulevard about 2:30 p.m. Thursday. Nestel said the man was wearing the same jacket - which was multicolored with a Taj Mahal emblem on the back - and police recovered the victim's cellphone.
Police did not release the suspect's name, but said he may be homeless. He is to be charged with aggravated assault, robbery and related offenses.
The victim suffered minor bumps and bruises.
The attack comes in the wake of two incidents in New York City in which passengers were thrown in front of oncoming trains and fatally struck.
"It is horrifying, and when you see that happen, you think the worst," Nestel said. "We all know there's a tremendous electrical source down there - the third rail. If you touch that third rail, you die.
"Somebody was on her side that day," he added.
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