Zeph, George and Valen started walking at the same time from the same starting point round a circular track. Valen walked in the clockwise direction. Zeph and George walked in an anti-clockwise direction. Valen took 12 min to complete each round. He met Zeph after every 2 minutes. He met George after every 6 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 Zeph met again at the starting point after 1 h, George 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 ÷ 12
= 5

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

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

Valen's distance : Zeph's distance
2 : 12 - 2
2 : 10

Valen's distance : George's distance
6 : 12 - 6
6 : 6

Valen	Zeph	George
2x3	10x3
6x1		6x1
6	30	6

The distance of Valen is the repeated identity. 
LCM of 2 and 6 = 6

In 1 h
Valen's rounds : Zeph's rounds : George's rounds
6 : 30 : 6

Distance that George completed in 1 h = 1.8 km

6 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 6 = 300 m

Circumference of the circular track = 300 m

Answer(s): (a) 5; (b) 300 m