Question

If three runners, A, B and C, start simultaneously from the same point and run around a circular track of length 500 m, in the same direction, at speeds of 5 kmph, 8 kmph and 15 kmph respectively, what is the time taken by them to meet for the first time?

Answer 1

18 minutes

Explanation:

Runner A: 5 km/h

Runner B: 8 km/h

Runner C: 15 km/h

speed = distance/time

time × speed = distance

time = distance/time

Runner A:

time = 500 m / (5 km/h) = 0.5 km / (5 km/h) = 0.1 h = 6 minutes

Runner B:

time = 500 m /(8 km/h) = 0.5 km / (8 km/h) = 0.06 h = 3.6 minutes

Runner C:

time = 500 m / (15 km/h) = 0.5 km / (15 km/h) = 0.0333 h = 2 minutes

Runners A, B, and C take 6 minutes, 3.6 minutes, and 2 minutes, respectively, to run 1 lap around the track.

Now we need the least common multiple of 6, 3.6, and 2.

Start with multiples of 6:

6

6/3.6 = 1.666 does not work.

12

12/3.6 = 3.333 does not work.

18

18/3.6 = 5 works

18 is a multiple of 6, 3.6, and 2.

Answer: 18 minutes