Three men start together to travel the same way around a circular track of 11 km. Their speeds are 4, 5-5 and 8 kmph respectively. When will they meet at the starting point for the first time?

Compute each man's lap time using time = distance/speed [1]. For an 11 km track the times are: 11/4 = 11/4 hours (2.75 h), 11/5.5 = 2 hours, and 11/8 = 11/8 hours (1.375 h). To find when all three are simultaneously at the start, take the LCM of these times. Treating them as fractions, LCM = LCM(numerators) / GCD(denominators). Numerators 11, 2, 11 give LCM = 22; denominators 4, 1, 8 give GCD = 1, so the LCM time = 22/1 = 22 hours. Thus they first meet together at the starting point after 22 hours.

Sources

1. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > 8.3 Speed > p. 113