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

1. How many rounds did Ken complete in 1 h?
2. When Ken and John met again at the starting point after 1 h, Perry had completed 1.8 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Ken's distance : John's distance
3 : 6 - 3
3 : 3

Ken's distance : Perry's distance
4 : 6 - 4
4 : 2

Ken	John	Perry
3x4	3x4
4x3		2x3
12	12	6

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

In 1 h
Ken's rounds : John's rounds : Perry's rounds
12 : 12 : 6

Distance that Perry completed in 1 h = 1.8 km

6 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 3 = 300 m

Circumference of the circular track = 300 m

Answer(s): (a) 10; (b) 300 m