Single correct option
A and B start running simultaneously from the same point on a circular track of length 600 m, in the same direction, at 5 m/s and 3 m/s respectively. After how many seconds will they meet at the starting point for the first time?
- A. 120
- B. 300
- C. 600
- D. 1200
Show answer and solution
Answer: (C) 600
A completes a lap in 600/5 = 120 s; B in 600/3 = 200 s.
A is at the start at 120, 240, 360, ...; B at 200, 400, 600, .... Both are there together first at LCM(120, 200) = 600 s.
Why not 300 s? At 300 s they meet (relative speed 2 m/s closes a 600 m gap), but at that moment A has run 1,500 m = 2.5 laps, so the meeting point is halfway round the track, not the start.
Tip: 'First meeting anywhere' uses relative speed; 'first meeting at the start' uses the LCM of lap times.
A is at the start at 120, 240, 360, ...; B at 200, 400, 600, .... Both are there together first at LCM(120, 200) = 600 s.
Why not 300 s? At 300 s they meet (relative speed 2 m/s closes a 600 m gap), but at that moment A has run 1,500 m = 2.5 laps, so the meeting point is halfway round the track, not the start.
Tip: 'First meeting anywhere' uses relative speed; 'first meeting at the start' uses the LCM of lap times.
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