The Boston School Committee voted unanimously Wednesday night to approve a new systemwide schedule that will allow most teenagers in the district to sleep in a bit next year.

Under the new framework, most high schools will start at or after 8 a.m. Presently, about half of the district’s public schools start class at or before 7:30 a.m. And whenever possible, younger children will be dismissed before 4 p.m., in part to prevent them from running out of steam late in the day — or walking home in the dark.