Luis, Vincent and Will started walking at the same time from the same starting point round a circular track. Will walked in the clockwise direction. Luis and Vincent walked in an anti-clockwise direction. Will took 6 min to complete each round. He met Luis after every 2 minutes. He met Vincent after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Will complete in 1 h?
2. When Will and Luis met again at the starting point after 1 h, Vincent had completed 2.6 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Will's distance : Luis's distance
2 : 6 - 2
2 : 4

Will's distance : Vincent's distance
4 : 6 - 4
4 : 2

Will	Luis	Vincent
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Will's rounds : Luis's rounds : Vincent's rounds
4 : 8 : 2

Distance that Vincent completed in 1 h = 2.6 km

2 rounds = 2.6 km = 2600 m

1 round = 2600 ÷ 2 = 1300 m

Circumference of the circular track = 1300 m

Answer(s): (a) 10; (b) 1300 m