Reggie, Zane and Ryan started walking at the same time from the same starting point round a circular track. Ryan walked in the clockwise direction. Reggie and Zane walked in an anti-clockwise direction. Ryan took 12 min to complete each round. He met Reggie after every 2 minutes. He met Zane 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 Reggie met again at the starting point after 1 h, Zane had completed 2.8 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 : Reggie's distance
2 : 12 - 2
2 : 10

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

Ryan	Reggie	Zane
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 : Reggie's rounds : Zane's rounds
14 : 70 : 10

Distance that Zane completed in 1 h = 2.8 km

10 rounds = 2.8 km = 2800 m

1 round = 2800 ÷ 10 = 280 m

Circumference of the circular track = 280 m

Answer(s): (a) 5; (b) 280 m