Julian, Rael and Valen started walking at the same time from the same starting point round a circular track. Valen walked in the clockwise direction. Julian and Rael walked in an anti-clockwise direction. Valen took 6 min to complete each round. He met Julian after every 4 minutes. He met Rael after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Valen complete in 1 h?
2. When Valen and Julian met again at the starting point after 1 h, Rael had completed 1.8 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Valen's distance : Julian's distance
4 : 6 - 4
4 : 2

Valen's distance : Rael's distance
5 : 6 - 5
5 : 1

Valen	Julian	Rael
4x5	2x5
5x4		1x4
20	10	4

The distance of Valen is the repeated identity. 
LCM of 4 and 5 = 20

In 1 h
Valen's rounds : Julian's rounds : Rael's rounds
20 : 10 : 4

Distance that Rael completed in 1 h = 1.8 km

4 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 4 = 450 m

Circumference of the circular track = 450 m

Answer(s): (a) 10; (b) 450 m