Paul, Cole and Warren started walking at the same time from the same starting point round a circular track. Warren walked in the clockwise direction. Paul and Cole walked in an anti-clockwise direction. Warren took 12 min to complete each round. He met Paul after every 2 minutes. He met Cole after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

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

(a)
1 h = 60 min

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

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

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

Warren's distance : Paul's distance
2 : 12 - 2
2 : 10

Warren's distance : Cole's distance
4 : 12 - 4
4 : 8

Warren	Paul	Cole
2x2	10x2
4x1		8x1
4	20	8

The distance of Warren is the repeated identity. 
LCM of 2 and 4 = 4

In 1 h
Warren's rounds : Paul's rounds : Cole's rounds
4 : 20 : 8

Distance that Cole completed in 1 h = 1.8 km

8 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 8 = 225 m

Circumference of the circular track = 225 m

Answer(s): (a) 5; (b) 225 m