Billy, Pierre and Jack started walking at the same time from the same starting point round a circular track. Jack walked in the clockwise direction. Billy and Pierre walked in an anti-clockwise direction. Jack took 6 min to complete each round. He met Billy after every 4 minutes. He met Pierre after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Jack complete in 1 h?
2. When Jack and Billy met again at the starting point after 1 h, Pierre had completed 2.1 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Jack's distance : Billy's distance
4 : 6 - 4
4 : 2

Jack's distance : Pierre's distance
5 : 6 - 5
5 : 1

Jack	Billy	Pierre
4x5	2x5
5x4		1x4
20	10	4

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

In 1 h
Jack's rounds : Billy's rounds : Pierre's rounds
20 : 10 : 4

Distance that Pierre completed in 1 h = 2.1 km

4 rounds = 2.1 km = 2100 m

1 round = 2100 ÷ 4 = 525 m

Circumference of the circular track = 525 m

Answer(s): (a) 10; (b) 525 m