John, Michael and Ben started walking at the same time from the same starting point round a circular track. Ben walked in the clockwise direction. John and Michael walked in an anti-clockwise direction. Ben took 12 min to complete each round. He met John after every 3 minutes. He met Michael after every 6 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 John met again at the starting point after 1 h, Michael had completed 2.4 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 ÷ 12
= 5

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

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

Ben's distance : John's distance
3 : 12 - 3
3 : 9

Ben's distance : Michael's distance
6 : 12 - 6
6 : 6

Ben	John	Michael
3x2	9x2
6x1		6x1
6	18	6

The distance of Ben is the repeated identity. 
LCM of 3 and 6 = 6

In 1 h
Ben's rounds : John's rounds : Michael's rounds
6 : 18 : 6

Distance that Michael completed in 1 h = 2.4 km

6 rounds = 2.4 km = 2400 m

1 round = 2400 ÷ 6 = 400 m

Circumference of the circular track = 400 m

Answer(s): (a) 5; (b) 400 m