Estimating the angle covered by the star trails and deducing how long the exposure lasted

The answer is given here. One minute of time corresponds to 15 arcminutes (written as 15'). This is because in 24 h the Earth revolves 360º, so
$$textrm{angle per time} = frac{360º}{24 textrm{ h}} =frac{21,600'}{1440 textrm{ min}} = 15'/textrm{min}.$$
If you turn this fraction upside down, you see that 1' corresponds to 1/15 min, or 4 seconds.

That is, you measure the angle (let's call it $theta$) of any of the star traces, as seen from the center (notice that the Northern Star is not exactly at the center, so that it itself traces a tiny arc instead of a dot). From the picture below, I get roughly $theta = 135º$. The exposure time is thus:
$$t_mathrm{exp} = frac{theta}{textrm{angle per time}} = frac{135º}{360º/24 textrm{ h}} sim 9textrm{ h}.$$

By the way, if you mark the position of the ends of the trails, you can recover the stellar sky. I found Ursa Major, marked by the yellow dots.