Valen, Daniel and Owen started walking at the same time from the same starting point round a circular track. Owen walked in the clockwise direction. Valen and Daniel walked in an anti-clockwise direction. Owen took 5 min to complete each round. He met Valen after every 3 minutes. He met Daniel after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Owen complete in 1 h?
2. When Owen and Valen met again at the starting point after 1 h, Daniel had completed 2.7 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

(b)
Owen took 5 min to complete 1 round
1 min = ¹₅ of circular track = 1 u
5 min = ⁵₅ of circular track = 5 u

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

Owen's distance : Valen's distance
3 : 5 - 3
3 : 2

Owen's distance : Daniel's distance
4 : 5 - 4
4 : 1

Owen	Valen	Daniel
3x4	2x4
4x3		1x3
12	8	3

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

In 1 h
Owen's rounds : Valen's rounds : Daniel's rounds
12 : 8 : 3

Distance that Daniel completed in 1 h = 2.7 km

3 rounds = 2.7 km = 2700 m

1 round = 2700 ÷ 3 = 900 m

Circumference of the circular track = 900 m

Answer(s): (a) 12; (b) 900 m