Glen, Xavier and Eric started walking at the same time from the same starting point round a circular track. Eric walked in the clockwise direction. Glen and Xavier walked in an anti-clockwise direction. Eric took 12 min to complete each round. He met Glen after every 3 minutes. He met Xavier after every 6 minutes. The three friends kept to their respective speeds throughout their walk.

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

(a)
1 h = 60 min

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

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

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

Eric's distance : Glen's distance
3 : 12 - 3
3 : 9

Eric's distance : Xavier's distance
6 : 12 - 6
6 : 6

Eric	Glen	Xavier
3x2	9x2
6x1		6x1
6	18	6

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

In 1 h
Eric's rounds : Glen's rounds : Xavier's rounds
6 : 18 : 6

Distance that Xavier completed in 1 h = 1.8 km

6 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 6 = 300 m

Circumference of the circular track = 300 m

Answer(s): (a) 5; (b) 300 m