David, Ken and Ivan started walking at the same time from the same starting point round a circular track. Ivan walked in the clockwise direction. David and Ken walked in an anti-clockwise direction. Ivan took 6 min to complete each round. He met David after every 4 minutes. He met Ken after every 5 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 David met again at the starting point after 1 h, Ken had completed 1.8 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 ÷ 6
= 10

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

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

Ivan's distance : David's distance
4 : 6 - 4
4 : 2

Ivan's distance : Ken's distance
5 : 6 - 5
5 : 1

Ivan	David	Ken
4x5	2x5
5x4		1x4
20	10	4

The distance of Ivan is the repeated identity. 
LCM of 4 and 5 = 20

In 1 h
Ivan's rounds : David's rounds : Ken's rounds
20 : 10 : 4

Distance that Ken completed in 1 h = 1.8 km

4 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 4 = 450 m

Circumference of the circular track = 450 m

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