Numerical answer
A, B and C start running at the same time from the same point on a circular track of length 600 m. A and B run clockwise at 5 m/s and 3 m/s respectively, while C runs anticlockwise at 7 m/s. After how many seconds will all three meet for the first time?
Show answer and solution
Answer: 300
Two runners meet every (track length)/(relative speed) seconds.
A and B (same direction): relative speed 2 m/s → meet every 600/2 = 300 s.
A and C (opposite): relative speed 12 m/s → every 50 s.
B and C (opposite): relative speed 10 m/s → every 60 s.
All three meet at the LCM of 300, 50 and 60 = 300 seconds.
Note this is different from meeting at the *starting point*, which requires the LCM of individual lap times (120, 200 and 600/7 s) = 600 s.
Tip: For first meeting anywhere, use LCM of pairwise meeting intervals.
A and B (same direction): relative speed 2 m/s → meet every 600/2 = 300 s.
A and C (opposite): relative speed 12 m/s → every 50 s.
B and C (opposite): relative speed 10 m/s → every 60 s.
All three meet at the LCM of 300, 50 and 60 = 300 seconds.
Note this is different from meeting at the *starting point*, which requires the LCM of individual lap times (120, 200 and 600/7 s) = 600 s.
Tip: For first meeting anywhere, use LCM of pairwise meeting intervals.
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