Owen, Charlie and Mark started walking at the same time from the same starting point round a circular track. Mark walked in the clockwise direction. Owen and Charlie walked in an anti-clockwise direction. Mark took 6 min to complete each round. He met Owen after every 3 minutes. He met Charlie after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

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

(a)
1 h = 60 min

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

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

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

Mark's distance : Owen's distance
3 : 6 - 3
3 : 3

Mark's distance : Charlie's distance
4 : 6 - 4
4 : 2

Mark	Owen	Charlie
3x4	3x4
4x3		2x3
12	12	6

The distance of Mark is the repeated identity. 
LCM of 3 and 4 = 12

In 1 h
Mark's rounds : Owen's rounds : Charlie's rounds
12 : 12 : 6

Distance that Charlie completed in 1 h = 1.5 km

6 rounds = 1.5 km = 1500 m

1 round = 1500 ÷ 3 = 250 m

Circumference of the circular track = 250 m

Answer(s): (a) 10; (b) 250 m