Reggie, Sam and Ian started walking at the same time from the same starting point round a circular track. Ian walked in the clockwise direction. Reggie and Sam walked in an anti-clockwise direction. Ian took 5 min to complete each round. He met Reggie after every 3 minutes. He met Sam after every 4 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 Reggie met again at the starting point after 1 h, Sam 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 ÷ 5
= 12

(b)
Ian took 5 min to complete 1 round
1 min = ¹₅ of circular track = 1 u
5 min = ⁵₅ of circular track = 5 u

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

Ian's distance : Reggie's distance
3 : 5 - 3
3 : 2

Ian's distance : Sam's distance
4 : 5 - 4
4 : 1

Ian	Reggie	Sam
3x4	2x4
4x3		1x3
12	8	3

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

In 1 h
Ian's rounds : Reggie's rounds : Sam's rounds
12 : 8 : 3

Distance that Sam completed in 1 h = 2.4 km

3 rounds = 2.4 km = 2400 m

1 round = 2400 ÷ 3 = 800 m

Circumference of the circular track = 800 m

Answer(s): (a) 12; (b) 800 m