Will, Ryan and Brandon started walking at the same time from the same starting point round a circular track. Brandon walked in the clockwise direction. Will and Ryan walked in an anti-clockwise direction. Brandon took 12 min to complete each round. He met Will after every 2 minutes. He met Ryan after every 7 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 Will met again at the starting point after 1 h, Ryan 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 ÷ 12
= 5

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

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

Brandon's distance : Will's distance
2 : 12 - 2
2 : 10

Brandon's distance : Ryan's distance
7 : 12 - 7
7 : 5

Brandon	Will	Ryan
2x7	10x7
7x2		5x2
14	70	10

The distance of Brandon is the repeated identity. 
LCM of 2 and 7 = 14

In 1 h
Brandon's rounds : Will's rounds : Ryan's rounds
14 : 70 : 10

Distance that Ryan completed in 1 h = 2.3 km

10 rounds = 2.3 km = 2300 m

1 round = 2300 ÷ 10 = 230 m

Circumference of the circular track = 230 m

Answer(s): (a) 5; (b) 230 m