Question 21
Ali and Barry went running on a standard $400$ metre track. They started simultaneously at the same location on the track but ran in opposite directions. Coincidentally, after $24$ minutes, they ended at the same location where they started. Ali completed $12$ rounds of the track in those $24$ minutes while Barry completed $10$ rounds. How many times did Ali and Barry pass each other during the run? (Exclude from your answer the times that they met at the start of the run and when they completed the run after $24$ minutes.)