Charlie, Gabriel and Justin started walking at the same time from the same starting point round a circular track. Justin walked in the clockwise direction. Charlie and Gabriel walked in an anti-clockwise direction. Justin took 6 min to complete each round. He met Charlie after every 2 minutes. He met Gabriel after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Justin complete in 1 h?
2. When Justin and Charlie met again at the starting point after 1 h, Gabriel had completed 2.5 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Justin's distance : Charlie's distance
2 : 6 - 2
2 : 4

Justin's distance : Gabriel's distance
5 : 6 - 5
5 : 1

Justin	Charlie	Gabriel
2x5	4x5
5x2		1x2
10	20	2

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

In 1 h
Justin's rounds : Charlie's rounds : Gabriel's rounds
10 : 20 : 2

Distance that Gabriel completed in 1 h = 2.5 km

2 rounds = 2.5 km = 2500 m

1 round = 2500 ÷ 2 = 1250 m

Circumference of the circular track = 1250 m

Answer(s): (a) 10; (b) 1250 m