To develop this problem, we simply have to make a relationship between speeds. This is because the echo of the sound is traveling a distance equal to that which the light travels.
We must calculate how much is that relationship of round trips between the two, as well
[tex]N = \frac{c}{s}[/tex]
Where
c = Speed of light
s = Speed of sound
By definition we know that
[tex]c = 3*10^8m/s[/tex]
[tex]s = 342,2m/s[/tex](Normal conditions)
Then,
[tex]N = \frac{3*10^8m/s}{342,2m/s}[/tex]
[tex]N = 876680.3[/tex]
Therefore the flash of the gunshot travel the round-trip distance between the mirror around to 876680.3 times before the echo of the gunshot is heard.
