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

1. How many rounds did Elijah complete in 1 h?
2. When Elijah and Albert met again at the starting point after 1 h, Ethan had completed 1.8 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Elijah's distance : Albert's distance
2 : 12 - 2
2 : 10

Elijah's distance : Ethan's distance
6 : 12 - 6
6 : 6

Elijah	Albert	Ethan
2x3	10x3
6x1		6x1
6	30	6

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

In 1 h
Elijah's rounds : Albert's rounds : Ethan's rounds
6 : 30 : 6

Distance that Ethan completed in 1 h = 1.8 km

6 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 6 = 300 m

Circumference of the circular track = 300 m

Answer(s): (a) 5; (b) 300 m