moon and sun appear together

[louism]

How often, and for how long do the sun and moon appear in the sky at the same time?

[Clanad]

Often asked and answered, such as here:
http://www.theanswerbank.co.uk/Science/Questio n268486.html

[mibn2cweus]

The Moon is in the daytime sky at some time almost every day! Now for the not so bad news:

The illuminated side of a New Moon is facing the Sun and is lost in its glare for a couple of days before and after. However, with careful observation you can find a waning crescent Moon a few days before or the sliver of a waxing Moon a few days after, although they are more impressive when seen just before Sunrise in the East or after Sunset in the West, respectively.

A Full Moon can sometimes be seen for a moment, opposite the Sun, under ideal viewing conditions, (a high place with an unobstructed view of both horizons and a little help from the refractive nature of the atmosphere), but this is a rare feat.

Other than a new or full Moon the biggest factor determining how often and how long the Moon is visible during the daytime (or nighttime) is how much of the sky is unobstructed by buildings, trees, mountains, clouds, etc.

Theoretically, the fraction of time the Moon shares the sky with the Sun is inversely proportional to how much of the Moon's illuminated side is facing the Earth.