Zane, Ian and Sean started walking at the same time from the same starting point round a circular track. Sean walked in the clockwise direction. Zane and Ian walked in an anti-clockwise direction. Sean took 6 min to complete each round. He met Zane after every 3 minutes. He met Ian after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Sean complete in 1 h?
2. When Sean and Zane met again at the starting point after 1 h, Ian had completed 2.7 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Sean's distance : Zane's distance
3 : 6 - 3
3 : 3

Sean's distance : Ian's distance
4 : 6 - 4
4 : 2

Sean	Zane	Ian
3x4	3x4
4x3		2x3
12	12	6

The distance of Sean is the repeated identity. 
LCM of 3 and 4 = 12

In 1 h
Sean's rounds : Zane's rounds : Ian's rounds
12 : 12 : 6

Distance that Ian completed in 1 h = 2.7 km

6 rounds = 2.7 km = 2700 m

1 round = 2700 ÷ 3 = 450 m

Circumference of the circular track = 450 m

Answer(s): (a) 10; (b) 450 m