Gabriel, Perry and Liam started walking at the same time from the same starting point round a circular track. Liam walked in the clockwise direction. Gabriel and Perry walked in an anti-clockwise direction. Liam took 12 min to complete each round. He met Gabriel after every 2 minutes. He met Perry after every 6 minutes. The three friends kept to their respective speeds throughout their walk.

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

(a)
1 h = 60 min

Number of rounds that Liam completed in 1 h
= 60 ÷ 12
= 5

(b)
Liam took 12 min to complete 1 round
1 min = ¹₁₂ of circular track = 1 u
12 min = ¹²₁₂ of circular track = 12 u

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

Liam's distance : Gabriel's distance
2 : 12 - 2
2 : 10

Liam's distance : Perry's distance
6 : 12 - 6
6 : 6

Liam	Gabriel	Perry
2x3	10x3
6x1		6x1
6	30	6

The distance of Liam is the repeated identity. 
LCM of 2 and 6 = 6

In 1 h
Liam's rounds : Gabriel's rounds : Perry's rounds
6 : 30 : 6

Distance that Perry completed in 1 h = 2.1 km

6 rounds = 2.1 km = 2100 m

1 round = 2100 ÷ 6 = 350 m

Circumference of the circular track = 350 m

Answer(s): (a) 5; (b) 350 m