Tom, Warren and Ken started walking at the same time from the same starting point round a circular track. Ken walked in the clockwise direction. Tom and Warren walked in an anti-clockwise direction. Ken took 6 min to complete each round. He met Tom after every 3 minutes. He met Warren after every 5 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 Tom met again at the starting point after 1 h, Warren had completed 2.4 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 : Tom's distance
3 : 6 - 3
3 : 3

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

Ken	Tom	Warren
3x5	3x5
5x3		1x3
15	15	3

The distance of Ken is the repeated identity. 
LCM of 3 and 5 = 15

In 1 h
Ken's rounds : Tom's rounds : Warren's rounds
15 : 15 : 3

Distance that Warren 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) 10; (b) 800 m