Simon, Lee and Warren started walking at the same time from the same starting point round a circular track. Warren walked in the clockwise direction. Simon and Lee walked in an anti-clockwise direction. Warren took 12 min to complete each round. He met Simon after every 2 minutes. He met Lee after every 6 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 Simon met again at the starting point after 1 h, Lee had completed 1.5 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 : Simon's distance
2 : 12 - 2
2 : 10

Warren's distance : Lee's distance
6 : 12 - 6
6 : 6

Warren	Simon	Lee
2x3	10x3
6x1		6x1
6	30	6

The distance of Warren is the repeated identity. 
LCM of 2 and 6 = 6

In 1 h
Warren's rounds : Simon's rounds : Lee's rounds
6 : 30 : 6

Distance that Lee completed in 1 h = 1.5 km

6 rounds = 1.5 km = 1500 m

1 round = 1500 ÷ 6 = 250 m

Circumference of the circular track = 250 m

Answer(s): (a) 5; (b) 250 m