Sean, Simon and Will started walking at the same time from the same starting point round a circular track. Will walked in the clockwise direction. Sean and Simon walked in an anti-clockwise direction. Will took 6 min to complete each round. He met Sean after every 3 minutes. He met Simon after every 5 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 Sean met again at the starting point after 1 h, Simon had completed 2.1 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 : Sean's distance
3 : 6 - 3
3 : 3

Will's distance : Simon's distance
5 : 6 - 5
5 : 1

Will	Sean	Simon
3x5	3x5
5x3		1x3
15	15	3

The distance of Will is the repeated identity. 
LCM of 3 and 5 = 15

In 1 h
Will's rounds : Sean's rounds : Simon's rounds
15 : 15 : 3

Distance that Simon completed in 1 h = 2.1 km

3 rounds = 2.1 km = 2100 m

1 round = 2100 ÷ 3 = 700 m

Circumference of the circular track = 700 m

Answer(s): (a) 10; (b) 700 m