Justin, Fred and Simon started walking at the same time from the same starting point round a circular track. Simon walked in the clockwise direction. Justin and Fred walked in an anti-clockwise direction. Simon took 6 min to complete each round. He met Justin after every 2 minutes. He met Fred 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 Justin met again at the starting point after 1 h, Fred had completed 1.3 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 : Justin's distance
2 : 6 - 2
2 : 4

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

Simon	Justin	Fred
2x5	4x5
5x2		1x2
10	20	2

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

In 1 h
Simon's rounds : Justin's rounds : Fred's rounds
10 : 20 : 2

Distance that Fred completed in 1 h = 1.3 km

2 rounds = 1.3 km = 1300 m

1 round = 1300 ÷ 2 = 650 m

Circumference of the circular track = 650 m

Answer(s): (a) 10; (b) 650 m