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

1. How many rounds did Valen complete in 1 h?
2. When Valen and Zane met again at the starting point after 1 h, Justin had completed 1.8 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

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

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

Valen	Zane	Justin
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Valen's rounds : Zane's rounds : Justin's rounds
4 : 8 : 2

Distance that Justin completed in 1 h = 1.8 km

2 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 2 = 900 m

Circumference of the circular track = 900 m

Answer(s): (a) 10; (b) 900 m