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

1. How many rounds did Ken complete in 1 h?
2. When Ken and Vaidev met again at the starting point after 1 h, Archie had completed 2.2 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

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

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

Ken	Vaidev	Archie
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Ken's rounds : Vaidev's rounds : Archie's rounds
4 : 8 : 2

Distance that Archie completed in 1 h = 2.2 km

2 rounds = 2.2 km = 2200 m

1 round = 2200 ÷ 2 = 1100 m

Circumference of the circular track = 1100 m

Answer(s): (a) 10; (b) 1100 m