At latitude $40^ ext{circ}$ North, how long does it take the Moon to traverse the sky?

About 12 hours, even if invisible due to being up during the day.

For observers situated at mid-latitudes, such as $40^ ext{circ}$ North, the Moon's visibility behavior is fundamentally different from that at the poles. At these latitudes, the Moon consistently follows the familiar pattern of rising and setting due to the way the celestial sphere appears to rotate relative to the observer. Regardless of whether the Moon is visible to the naked eye (i.e., not in the New Moon phase, which means it is up during daylight hours), it still traverses the sky along an arc and completes its transit in approximately 12 hours. The limiting factor at mid-latitudes is the phase of the Moon relative to the day/night cycle, not the horizon blocking its entire path.