Vincent, Luke and Ben started walking at the same time from the same starting point round a circular track. Ben walked in the clockwise direction. Vincent and Luke walked in an anti-clockwise direction. Ben took 12 min to complete each round. He met Vincent after every 2 minutes. He met Luke after every 4 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 Vincent met again at the starting point after 1 h, Luke 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 : Vincent's distance
2 : 12 - 2
2 : 10

Ben's distance : Luke's distance
4 : 12 - 4
4 : 8

Ben	Vincent	Luke
2x2	10x2
4x1		8x1
4	20	8

The distance of Ben is the repeated identity. 
LCM of 2 and 4 = 4

In 1 h
Ben's rounds : Vincent's rounds : Luke's rounds
4 : 20 : 8

Distance that Luke completed in 1 h = 2.4 km

8 rounds = 2.4 km = 2400 m

1 round = 2400 ÷ 8 = 300 m

Circumference of the circular track = 300 m

Answer(s): (a) 5; (b) 300 m