Ivan, Billy and Brandon started walking at the same time from the same starting point round a circular track. Brandon walked in the clockwise direction. Ivan and Billy walked in an anti-clockwise direction. Brandon took 6 min to complete each round. He met Ivan after every 2 minutes. He met Billy after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Brandon complete in 1 h?
2. When Brandon and Ivan met again at the starting point after 1 h, Billy had completed 2.3 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

Number of rounds that Brandon completed in 1 h
= 60 ÷ 6
= 10

(b)
Brandon took 6 min to complete 1 round
1 min = ¹₆ of circular track = 1 u
6 min = ⁶₆ of circular track = 6 u

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

Brandon's distance : Ivan's distance
2 : 6 - 2
2 : 4

Brandon's distance : Billy's distance
4 : 6 - 4
4 : 2

Brandon	Ivan	Billy
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Brandon's rounds : Ivan's rounds : Billy's rounds
4 : 8 : 2

Distance that Billy completed in 1 h = 2.3 km

2 rounds = 2.3 km = 2300 m

1 round = 2300 ÷ 2 = 1150 m

Circumference of the circular track = 1150 m

Answer(s): (a) 10; (b) 1150 m