Analyzing Movement Cycles

The goal is to determine the time when both A and B are simultaneously present at the starting point O.

Person A's Cycle Analysis:

• Time for one round: 9 minutes.
• Delay before restart: 1 minute.
• A arrives at O after completing rounds at the following times (T):
  • T = 9 minutes (End of Round 1)
  • T = (9 + 1) + 9 = 19 minutes (End of Round 2)
  • T = (19 + 1) + 9 = 29 minutes (End of Round 3)
  • And so on...

Person B's Cycle Analysis:

• Time for one round: 13 minutes.
• Delay before restart: 2 minutes.
• B arrives at O after completing rounds at the following times (T):
  • T = 13 minutes (End of Round 1)
  • T = (13 + 2) + 13 = 28 minutes (End of Round 2)
  • T = (28 + 2) + 13 = 43 minutes (End of Round 3)
  • And so on...

Determining the Meeting Time at O

We examine the arrival times at point O:

• At 29 minutes, A completes their 3rd round, arriving exactly at O.
• B completed their 2nd round at 28 minutes, arriving at O. B then entered a 2-minute delay period (from T=28 to T=30).

At the moment T=29 minutes, A is arriving at O. B, having arrived at T=28 minutes, is currently within its delay period at O. Given the provided options, this specific instance where A completes a round and B is present at O (during its delay) is considered the meeting time.

Thus, they meet again at O after 29 minutes.