Vaidev, Ian and Luis started walking at the same time from the same starting point round a circular track. Luis walked in the clockwise direction. Vaidev and Ian walked in an anti-clockwise direction. Luis took 6 min to complete each round. He met Vaidev after every 2 minutes. He met Ian after every 5 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 Vaidev met again at the starting point after 1 h, Ian had completed 2.6 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 : Vaidev's distance
2 : 6 - 2
2 : 4

Luis's distance : Ian's distance
5 : 6 - 5
5 : 1

Luis	Vaidev	Ian
2x5	4x5
5x2		1x2
10	20	2

The distance of Luis is the repeated identity. 
LCM of 2 and 5 = 10

In 1 h
Luis's rounds : Vaidev's rounds : Ian's rounds
10 : 20 : 2

Distance that Ian completed in 1 h = 2.6 km

2 rounds = 2.6 km = 2600 m

1 round = 2600 ÷ 2 = 1300 m

Circumference of the circular track = 1300 m

Answer(s): (a) 10; (b) 1300 m