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

1. How many rounds did Oscar complete in 1 h?
2. When Oscar and Charlie met again at the starting point after 1 h, Valen had completed 1.9 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Oscar's distance : Charlie's distance
2 : 6 - 2
2 : 4

Oscar's distance : Valen's distance
4 : 6 - 4
4 : 2

Oscar	Charlie	Valen
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Oscar's rounds : Charlie's rounds : Valen's rounds
4 : 8 : 2

Distance that Valen completed in 1 h = 1.9 km

2 rounds = 1.9 km = 1900 m

1 round = 1900 ÷ 2 = 950 m

Circumference of the circular track = 950 m

Answer(s): (a) 10; (b) 950 m