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

1. How many rounds did Seth complete in 1 h?
2. When Seth and Mark met again at the starting point after 1 h, Elijah had completed 2.4 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Seth's distance : Mark's distance
2 : 12 - 2
2 : 10

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

Seth	Mark	Elijah
2x3	10x3
6x1		6x1
6	30	6

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

In 1 h
Seth's rounds : Mark's rounds : Elijah's rounds
6 : 30 : 6

Distance that Elijah completed in 1 h = 2.4 km

6 rounds = 2.4 km = 2400 m

1 round = 2400 ÷ 6 = 400 m

Circumference of the circular track = 400 m

Answer(s): (a) 5; (b) 400 m