$1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur?
1. Let us introduce the following variables
$$x_B=L-x$$
$$t_A=t_B+\Delta t$$
2. Time of flight of $\gamma$-quantum to counters
$$t_B+\Delta t=\frac{x}{c}$$
$$t_B=\frac{L-x}{c}$$
3. Solving the equations together, we obtain
$$\frac{L-x}{c} + \Delta t = \frac{x}{c}$$
$$x= \frac{L+c\Delta t}{2}=1.15\,м$$
At a distance $1.15\, \text{m}$ from the microphone $A$