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

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

(a)
1 h = 60 min

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

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

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

Zeph's distance : Riordan's distance
2 : 6 - 2
2 : 4

Zeph's distance : Ken's distance
4 : 6 - 4
4 : 2

Zeph	Riordan	Ken
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Zeph's rounds : Riordan's rounds : Ken's rounds
4 : 8 : 2

Distance that Ken 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