Ken, Charlie and Oliver started walking at the same time from the same starting point round a circular track. Oliver walked in the clockwise direction. Ken and Charlie walked in an anti-clockwise direction. Oliver took 12 min to complete each round. He met Ken after every 2 minutes. He met Charlie after every 6 minutes. The three friends kept to their respective speeds throughout their walk.

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

(a)
1 h = 60 min

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

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

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

Oliver's distance : Ken's distance
2 : 12 - 2
2 : 10

Oliver's distance : Charlie's distance
6 : 12 - 6
6 : 6

Oliver	Ken	Charlie
2x3	10x3
6x1		6x1
6	30	6

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

In 1 h
Oliver's rounds : Ken's rounds : Charlie's rounds
6 : 30 : 6

Distance that Charlie completed in 1 h = 2.1 km

6 rounds = 2.1 km = 2100 m

1 round = 2100 ÷ 6 = 350 m

Circumference of the circular track = 350 m

Answer(s): (a) 5; (b) 350 m