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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time and Distance

Three runners start together from the same point of a circular track and run in the same direction at 4 m/s, 6 m/s and 10 m/s. The track is 240 m long. After how many seconds will all three first be together again at the starting point?

All three are first together at the starting point after 120 seconds. Their lap times are 60, 40 and 24 seconds, and the first common moment is the LCM of these numbers. The LCM is 120, when they have run 2, 3 and 5 laps.

  1. A120 secondsCorrect
  2. B60 seconds
  3. C240 seconds
  4. D40 seconds

Explanation

Times to complete one lap are 240/4 = 60 s, 240/6 = 40 s and 240/10 = 24 s. They are together at the start when time is a common multiple of 60, 40 and 24. LCM of 60, 40, 24: 60 = 2^2x3x5, 40 = 2^3x5, 24 = 2^3x3, so LCM = 2^3x3x5 = 120 s. Check: 120 s gives 2, 3 and 5 laps respectively. The answer 60 s fails because the 40 s and 24 s runners are not at a whole lap then.

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