Riordan, Peter and Ivan started walking at the same time from the same starting point round a circular track. Ivan walked in the clockwise direction. Riordan and Peter walked in an anti-clockwise direction. Ivan took 5 min to complete each round. He met Riordan after every 3 minutes. He met Peter after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

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

(a)
1 h = 60 min

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

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

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

Ivan's distance : Riordan's distance
3 : 5 - 3
3 : 2

Ivan's distance : Peter's distance
4 : 5 - 4
4 : 1

Ivan	Riordan	Peter
3x4	2x4
4x3		1x3
12	8	3

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

In 1 h
Ivan's rounds : Riordan's rounds : Peter's rounds
12 : 8 : 3

Distance that Peter completed in 1 h = 2.7 km

3 rounds = 2.7 km = 2700 m

1 round = 2700 ÷ 3 = 900 m

Circumference of the circular track = 900 m

Answer(s): (a) 12; (b) 900 m