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

1. How many rounds did Sam complete in 1 h?
2. When Sam and Xavier met again at the starting point after 1 h, Ken had completed 2.2 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Sam's distance : Xavier's distance
2 : 12 - 2
2 : 10

Sam's distance : Ken's distance
4 : 12 - 4
4 : 8

Sam	Xavier	Ken
2x2	10x2
4x1		8x1
4	20	8

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

In 1 h
Sam's rounds : Xavier's rounds : Ken's rounds
4 : 20 : 8

Distance that Ken completed in 1 h = 2.2 km

8 rounds = 2.2 km = 2200 m

1 round = 2200 ÷ 8 = 275 m

Circumference of the circular track = 275 m

Answer(s): (a) 5; (b) 275 m