This was actually the first time Ryuutaro really got close to a school. The first nine years of his live he'd been taught by a private teacher (not even that was fully common in his world, parental teaching was usual) and after he ran away he just stopped learning school material all together. He could read, write and earn money, so what did it matter?
His curiosity was growing about this, though the concept of public schools still seemed almost weird to him (even though they did exist in his world just fine).
Once again he just pictured Hayato in this place, in the everyday life he used to have before they met, staying silent over all these thoughts for the moment being.