Zane, Andy and Ben started walking at the same time from the same starting point round a circular track. Ben walked in the clockwise direction. Zane and Andy walked in an anti-clockwise direction. Ben took 6 min to complete each round. He met Zane after every 2 minutes. He met Andy after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Ben complete in 1 h?
2. When Ben and Zane met again at the starting point after 1 h, Andy had completed 2.1 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Ben's distance : Zane's distance
2 : 6 - 2
2 : 4

Ben's distance : Andy's distance
5 : 6 - 5
5 : 1

Ben	Zane	Andy
2x5	4x5
5x2		1x2
10	20	2

The distance of Ben is the repeated identity. 
LCM of 2 and 5 = 10

In 1 h
Ben's rounds : Zane's rounds : Andy's rounds
10 : 20 : 2

Distance that Andy completed in 1 h = 2.1 km

2 rounds = 2.1 km = 2100 m

1 round = 2100 ÷ 2 = 1050 m

Circumference of the circular track = 1050 m

Answer(s): (a) 10; (b) 1050 m