Wesley, Ryan and Ian started walking at the same time from the same starting point round a circular track. Ian walked in the clockwise direction. Wesley and Ryan walked in an anti-clockwise direction. Ian took 12 min to complete each round. He met Wesley after every 3 minutes. He met Ryan after every 6 minutes. The three friends kept to their respective speeds throughout their walk.

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

(a)
1 h = 60 min

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

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

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

Ian's distance : Wesley's distance
3 : 12 - 3
3 : 9

Ian's distance : Ryan's distance
6 : 12 - 6
6 : 6

Ian	Wesley	Ryan
3x2	9x2
6x1		6x1
6	18	6

The distance of Ian is the repeated identity. 
LCM of 3 and 6 = 6

In 1 h
Ian's rounds : Wesley's rounds : Ryan's rounds
6 : 18 : 6

Distance that Ryan 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