Julian, Oscar and Michael started walking at the same time from the same starting point round a circular track. Michael walked in the clockwise direction. Julian and Oscar walked in an anti-clockwise direction. Michael took 6 min to complete each round. He met Julian after every 2 minutes. He met Oscar after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Michael complete in 1 h?
2. When Michael and Julian met again at the starting point after 1 h, Oscar had completed 2.7 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

Number of rounds that Michael completed in 1 h
= 60 ÷ 6
= 10

(b)
Michael took 6 min to complete 1 round
1 min = ¹₆ of circular track = 1 u
6 min = ⁶₆ of circular track = 6 u

Michael's distance is the repeated identity.
Make Michael's distance the same.

Michael's distance : Julian's distance
2 : 6 - 2
2 : 4

Michael's distance : Oscar's distance
5 : 6 - 5
5 : 1

Michael	Julian	Oscar
2x5	4x5
5x2		1x2
10	20	2

The distance of Michael is the repeated identity. 
LCM of 2 and 5 = 10

In 1 h
Michael's rounds : Julian's rounds : Oscar's rounds
10 : 20 : 2

Distance that Oscar completed in 1 h = 2.7 km

2 rounds = 2.7 km = 2700 m

1 round = 2700 ÷ 2 = 1350 m

Circumference of the circular track = 1350 m

Answer(s): (a) 10; (b) 1350 m