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

1. How many rounds did Paul complete in 1 h?
2. When Paul and Tom met again at the starting point after 1 h, Liam had completed 1.5 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Paul's distance : Tom's distance
3 : 5 - 3
3 : 2

Paul's distance : Liam's distance
4 : 5 - 4
4 : 1

Paul	Tom	Liam
3x4	2x4
4x3		1x3
12	8	3

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

In 1 h
Paul's rounds : Tom's rounds : Liam's rounds
12 : 8 : 3

Distance that Liam completed in 1 h = 1.5 km

3 rounds = 1.5 km = 1500 m

1 round = 1500 ÷ 3 = 500 m

Circumference of the circular track = 500 m

Answer(s): (a) 12; (b) 500 m