Pierre, Jeremy and Liam started walking at the same time from the same starting point round a circular track. Liam walked in the clockwise direction. Pierre and Jeremy walked in an anti-clockwise direction. Liam took 6 min to complete each round. He met Pierre after every 2 minutes. He met Jeremy after every 5 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 Pierre met again at the starting point after 1 h, Jeremy had completed 1.8 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 ÷ 6
= 10

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

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

Liam's distance : Pierre's distance
2 : 6 - 2
2 : 4

Liam's distance : Jeremy's distance
5 : 6 - 5
5 : 1

Liam	Pierre	Jeremy
2x5	4x5
5x2		1x2
10	20	2

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

In 1 h
Liam's rounds : Pierre's rounds : Jeremy's rounds
10 : 20 : 2

Distance that Jeremy completed in 1 h = 1.8 km

2 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 2 = 900 m

Circumference of the circular track = 900 m

Answer(s): (a) 10; (b) 900 m