Japheth, Peter and Zane started walking at the same time from the same starting point round a circular track. Zane walked in the clockwise direction. Japheth and Peter walked in an anti-clockwise direction. Zane took 12 min to complete each round. He met Japheth after every 3 minutes. He met Peter after every 6 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Zane complete in 1 h?
2. When Zane and Japheth met again at the starting point after 1 h, Peter had completed 2.1 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

Number of rounds that Zane completed in 1 h
= 60 ÷ 12
= 5

(b)
Zane took 12 min to complete 1 round
1 min = ¹₁₂ of circular track = 1 u
12 min = ¹²₁₂ of circular track = 12 u

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

Zane's distance : Japheth's distance
3 : 12 - 3
3 : 9

Zane's distance : Peter's distance
6 : 12 - 6
6 : 6

Zane	Japheth	Peter
3x2	9x2
6x1		6x1
6	18	6

The distance of Zane is the repeated identity. 
LCM of 3 and 6 = 6

In 1 h
Zane's rounds : Japheth's rounds : Peter's rounds
6 : 18 : 6

Distance that Peter completed in 1 h = 2.1 km

6 rounds = 2.1 km = 2100 m

1 round = 2100 ÷ 6 = 350 m

Circumference of the circular track = 350 m

Answer(s): (a) 5; (b) 350 m