Luke, Julian and Zeph started walking at the same time from the same starting point round a circular track. Zeph walked in the clockwise direction. Luke and Julian walked in an anti-clockwise direction. Zeph took 6 min to complete each round. He met Luke after every 2 minutes. He met Julian 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 Luke met again at the starting point after 1 h, Julian had completed 1.6 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 : Luke's distance
2 : 6 - 2
2 : 4

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

Zeph	Luke	Julian
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 : Luke's rounds : Julian's rounds
4 : 8 : 2

Distance that Julian completed in 1 h = 1.6 km

2 rounds = 1.6 km = 1600 m

1 round = 1600 ÷ 2 = 800 m

Circumference of the circular track = 800 m

Answer(s): (a) 10; (b) 800 m