John, Luis and Simon started walking at the same time from the same starting point round a circular track. Simon walked in the clockwise direction. John and Luis walked in an anti-clockwise direction. Simon took 6 min to complete each round. He met John after every 3 minutes. He met Luis after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Simon complete in 1 h?
2. When Simon and John met again at the starting point after 1 h, Luis had completed 2.1 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Simon's distance : John's distance
3 : 6 - 3
3 : 3

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

Simon	John	Luis
3x5	3x5
5x3		1x3
15	15	3

The distance of Simon is the repeated identity. 
LCM of 3 and 5 = 15

In 1 h
Simon's rounds : John's rounds : Luis's rounds
15 : 15 : 3

Distance that Luis completed in 1 h = 2.1 km

3 rounds = 2.1 km = 2100 m

1 round = 2100 ÷ 3 = 700 m

Circumference of the circular track = 700 m

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