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

1. How many rounds did Glen complete in 1 h?
2. When Glen and Rael met again at the starting point after 1 h, Zane had completed 1.5 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Glen's distance : Rael's distance
3 : 12 - 3
3 : 9

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

Glen	Rael	Zane
3x2	9x2
6x1		6x1
6	18	6

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

In 1 h
Glen's rounds : Rael's rounds : Zane's rounds
6 : 18 : 6

Distance that Zane completed in 1 h = 1.5 km

6 rounds = 1.5 km = 1500 m

1 round = 1500 ÷ 6 = 250 m

Circumference of the circular track = 250 m

Answer(s): (a) 5; (b) 250 m