But first, they had to get to know one another.
Harriton teacher Peter Crooke welcomed the guests and acknowledged that both groups were a little out of their comfort zones.
"This is a leap for us to have people come in from a neighborhood we're not familiar with. And for you, too, to come out to a neighborhood you're not familiar with," he said, motioning to the Philadelphia students.
But they got quickly down to business - an icebreaker, a tour of the school, a $100 million structure opened in 2009.
Harriton junior Carlie Ladda pointed out the cafeteria to Erica Irving, a senior from Bodine High, a magnet school in Northern Liberties.
"It's pretty good," Ladda said. "They have a sandwich bar - it's like a Wawa. They made whatever you want."
Irving nodded.
"This is like four times the size of our lunchroom, and that doubles as a gym," she said.
But the students found a lot of common ground, too - the sports they play, the clubs they participate in, colleges, dress codes.
Harriton junior Ilissa Kaye pointed out the theaterlike auditorium, the greenhouse, the lecture hall.
"Can you carry your bags in class here?" asked Aliyah Pressley, a junior at Mastery Charter School's Lenfest campus.
Kaye said they could.
"We can't," said Pressley. "You can't even get into the school with your jacket on."
The Philadelphia students said they liked the way teachers seemed to treat students with respect at Harriton.
But not everything was better at Harriton. TiJuana Jackson, another junior at Bodine, said that the Lower Merion school felt too big, with 1,000 students.
"I like our school because we know everybody," said Jackson. About 550 students attend Bodine.