Anecdotal from my grandfather: They had districts, and with many things it depended on distance / traffic. He felt the response times were decent enough in populated areas, with far less vehicle traffic than the 80's (when we talked about it). The NYPD covered something like 300+ square miles at that time.

He was in a "Radio car" (see radio motor patrol). They were a a different breed from a different time. They might just whack you upside the head for doing stupid stuff instead of taking you in. They'd spank little hooligans and take them home. They'd whack a parent or two as well. (Whack was the term for smacking them, as opposed to hitting/punching/fighting, which sometimes whacking led too. )