Cruising speed

"Faster, Higher, Stronger!"

(motto of the Olympic Games)

The renowned Jamaican sprinter Usain Bolt clinched two gold medals at the $2012$ Olympics in the $100$ and $200$ meters events.

These two distances are particularly significant because, through a scientific approach, they can help a coach determine the optimal lineup for the national team in the 4 \times 100 meters relay.

Given the short nature of these distances, the running strategy is straightforward: initially, the athlete accelerates to their maximum possible speed during a specific start period (acceleration time), and then continues the rest of the distance at this constant speed, referred to as cruising speed. Naturally, when assembling the relay team, the athlete with the best time in this distance should start, and for the remaining $3$ legs, three athletes with the best cruising speeds should be selected from the others.

The coach of your country's athletics team has enlisted your help, as one of the top programmers, to assist in forming the relay team. To provide swift assistance, you need to solve the following problem: given the athlete's times in the $100$ and $200$ meters events, determine their cruising speed. It is known that each athlete's cruising speed and acceleration time have remained constant during your analysis.