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

1. How many rounds did Jack complete in 1 h?
2. When Jack and Charlie met again at the starting point after 1 h, Andy had completed 2.4 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Jack's distance : Charlie's distance
3 : 12 - 3
3 : 9

Jack's distance : Andy's distance
6 : 12 - 6
6 : 6

Jack	Charlie	Andy
3x2	9x2
6x1		6x1
6	18	6

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

In 1 h
Jack's rounds : Charlie's rounds : Andy's rounds
6 : 18 : 6

Distance that Andy completed in 1 h = 2.4 km

6 rounds = 2.4 km = 2400 m

1 round = 2400 ÷ 6 = 400 m

Circumference of the circular track = 400 m

Answer(s): (a) 5; (b) 400 m