George, Flynn and Simon started walking at the same time from the same starting point round a circular track. Simon walked in the clockwise direction. George and Flynn walked in an anti-clockwise direction. Simon took 6 min to complete each round. He met George after every 2 minutes. He met Flynn after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Simon complete in 1 h?
2. When Simon and George met again at the starting point after 1 h, Flynn had completed 2.9 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Simon's distance : George's distance
2 : 6 - 2
2 : 4

Simon's distance : Flynn's distance
4 : 6 - 4
4 : 2

Simon	George	Flynn
2x2	4x2
4x1		2x1
4	8	2

The distance of Simon is the repeated identity. 
LCM of 2 and 4 = 4

In 1 h
Simon's rounds : George's rounds : Flynn's rounds
4 : 8 : 2

Distance that Flynn completed in 1 h = 2.9 km

2 rounds = 2.9 km = 2900 m

1 round = 2900 ÷ 2 = 1450 m

Circumference of the circular track = 1450 m

Answer(s): (a) 10; (b) 1450 m