Asher, Billy and Luis started walking at the same time from the same starting point round a circular track. Luis walked in the clockwise direction. Asher and Billy walked in an anti-clockwise direction. Luis took 12 min to complete each round. He met Asher after every 2 minutes. He met Billy after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

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

(a)
1 h = 60 min

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

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

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

Luis's distance : Asher's distance
2 : 12 - 2
2 : 10

Luis's distance : Billy's distance
4 : 12 - 4
4 : 8

Luis	Asher	Billy
2x2	10x2
4x1		8x1
4	20	8

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

In 1 h
Luis's rounds : Asher's rounds : Billy's rounds
4 : 20 : 8

Distance that Billy completed in 1 h = 1.8 km

8 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 8 = 225 m

Circumference of the circular track = 225 m

Answer(s): (a) 5; (b) 225 m