Question 8
Allen, Bob and Cindy are walking around a circular lake trail. They start walking from the same location at the same time. Bob is walking clockwise, while Cindy and Allen are walking counterclockwise. They all walk at constant speeds. After a while, Bob meets Cindy for the first time. Then $3$ minutes later, Bob meets Allen. Finally, another $14$ minutes later, Bob meets Cindy for the second time. It is known that Cindy’s speed is $\frac34$ of Bob’s speed and the lake trail is $2023$ metres long. How many minutes after Bob meets Cindy for the first time will Bob meet Allen for the second time?
**User-approved clarification (added condition, not official source wording):**
The Bob–Allen encounter described as occurring 3 minutes after Bob first meets Cindy is Bob and Allen's first meeting after they start.
**User-approved clarification (added condition, not official source wording):**
The Bob–Allen encounter described as occurring 3 minutes after Bob first meets Cindy is Bob and Allen's first meeting after they start.