Billy, Vincent and Luis started walking at the same time from the same starting point round a circular track. Luis walked in the clockwise direction. Billy and Vincent walked in an anti-clockwise direction. Luis took 6 min to complete each round. He met Billy after every 2 minutes. He met Vincent 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 Billy met again at the starting point after 1 h, Vincent had completed 1.4 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 ÷ 6
= 10

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

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

Luis's distance : Billy's distance
2 : 6 - 2
2 : 4

Luis's distance : Vincent's distance
4 : 6 - 4
4 : 2

Luis	Billy	Vincent
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Luis's rounds : Billy's rounds : Vincent's rounds
4 : 8 : 2

Distance that Vincent completed in 1 h = 1.4 km

2 rounds = 1.4 km = 1400 m

1 round = 1400 ÷ 2 = 700 m

Circumference of the circular track = 700 m

Answer(s): (a) 10; (b) 700 m