At my latitude (26°N) the zenith for noon changes about every 5 miles (8k) east or west of where I'm located, and the distance grows shorter the more north you go (at 45°N it's 3.8m/6.1k east/west). That's why time zones exist, to make this a tractable problem (although we somehow have managed to make a mess of time zones but that's another rant).

EDIT: my latitude was too precise for the distance mentioned. Simplified it.