7.2. Three cyclists leave the city. The speed of the first one is 12 km/h, the second one is 16 km/h, and the third one is 24 km/h. It is known that the first one was cycling exactly when the second and third were resting (standing still), and that at no time did two cyclists cycle simultaneously. It is also known that in 3 hours, all three covered the same distance. Find this distance.
Answer: 16 km

Solution: From the condition, it follows that each of the cyclists was riding at the time when the other two were standing, and, moreover, at any given moment, one of the cyclists was riding (the first one rode when the second and third were standing). Since they all traveled the same distance, and the ratio of their speeds is $3: 4: 6$, the time of movement for the first cyclist is 24 parts, for the second - 18 parts, and for the third - 12 parts of time. In total, they rode for 3 hours $=180$ minutes. Therefore, one part of time is $10 / 3$ minutes. Consequently, the first one rode for 80 minutes, which is $4 / 3$ hours. During this time, he traveled 16 km.

Comment: A correct answer without justification - 0 points.