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

1. How many rounds did Ryan complete in 1 h?
2. When Ryan and Ken met again at the starting point after 1 h, Owen had completed 2.5 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Ryan's distance : Ken's distance
2 : 12 - 2
2 : 10

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

Ryan	Ken	Owen
2x7	10x7
7x2		5x2
14	70	10

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

In 1 h
Ryan's rounds : Ken's rounds : Owen's rounds
14 : 70 : 10

Distance that Owen completed in 1 h = 2.5 km

10 rounds = 2.5 km = 2500 m

1 round = 2500 ÷ 10 = 250 m

Circumference of the circular track = 250 m

Answer(s): (a) 5; (b) 250 m