Dylan, Simon and Paul started walking at the same time from the same starting point round a circular track. Paul walked in the clockwise direction. Dylan and Simon walked in an anti-clockwise direction. Paul took 12 min to complete each round. He met Dylan after every 3 minutes. He met Simon after every 6 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 Dylan met again at the starting point after 1 h, Simon had completed 2.4 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 ÷ 12
= 5

(b)
Paul took 12 min to complete 1 round
1 min = ¹₁₂ of circular track = 1 u
12 min = ¹²₁₂ of circular track = 12 u

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

Paul's distance : Dylan's distance
3 : 12 - 3
3 : 9

Paul's distance : Simon's distance
6 : 12 - 6
6 : 6

Paul	Dylan	Simon
3x2	9x2
6x1		6x1
6	18	6

The distance of Paul is the repeated identity. 
LCM of 3 and 6 = 6

In 1 h
Paul's rounds : Dylan's rounds : Simon's rounds
6 : 18 : 6

Distance that Simon completed in 1 h = 2.4 km

6 rounds = 2.4 km = 2400 m

1 round = 2400 ÷ 6 = 400 m

Circumference of the circular track = 400 m

Answer(s): (a) 5; (b) 400 m