**Category:** Mechanics  
**Subtype:** Harmonic Motion (Oscillations)  
**Problem Description:** This problem involves two points oscillating harmonically along the horizontal axis (Ox) with given equations of motion. The task is to determine the ratio of the velocities of the two points at the moment they are farthest apart from each other.  

**Key Elements:**
- The equations of motion for the two points are provided.
- The first point's position is given by \(x_{1}=4 \cos (5 \pi t) \mathrm{cm}\).
- The second point's position is given by \(x_{2}=4 \sqrt{3} \cos \left(5 \pi t+\frac{\pi}{6}\right) \mathrm{cm}\).
- The problem requires finding the ratio of their velocities when they are at their maximum separation.

**Objective:** Find the ratio of the velocities of the first point to the second point at the moment they are farthest apart.