Owen, Fred and Oscar started walking at the same time from the same starting point round a circular track. Oscar walked in the clockwise direction. Owen and Fred walked in an anti-clockwise direction. Oscar took 12 min to complete each round. He met Owen after every 2 minutes. He met Fred after every 7 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Oscar complete in 1 h?
2. When Oscar and Owen met again at the starting point after 1 h, Fred had completed 2.9 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Oscar's distance : Owen's distance
2 : 12 - 2
2 : 10

Oscar's distance : Fred's distance
7 : 12 - 7
7 : 5

Oscar	Owen	Fred
2x7	10x7
7x2		5x2
14	70	10

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

In 1 h
Oscar's rounds : Owen's rounds : Fred's rounds
14 : 70 : 10

Distance that Fred completed in 1 h = 2.9 km

10 rounds = 2.9 km = 2900 m

1 round = 2900 ÷ 10 = 290 m

Circumference of the circular track = 290 m

Answer(s): (a) 5; (b) 290 m