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

A cyclist leaves Nagpur at 6 a.m. at 12 km/h. A motorcyclist leaves the same place along the same road at 8 a.m. at 30 km/h. At what time does the motorcyclist overtake the cyclist?

The motorcyclist overtakes at 9:20 a.m. The cyclist has a 24 km head start by 8 a.m., and the gap closes at the relative speed of 18 km/h. That takes 80 minutes, so the overtaking occurs 80 minutes after 8 a.m.

  1. A9:20 a.m.Correct
  2. B9:40 a.m.
  3. C10:00 a.m.
  4. D10:20 a.m.

Explanation

By 8 a.m. the cyclist is 24 km ahead. Relative speed = 30 - 12 = 18 km/h, so catching up takes 24/18 = 4/3 h = 80 minutes. 8:00 plus 80 minutes is 9:20 a.m. Check: the cyclist travels 12 x 3.333 = 40 km and the motorcyclist 30 x 1.333 = 40 km. Using the sum 42 km/h gives a wrong time.

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