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

1. How many rounds did Nick complete in 1 h?
2. When Nick and Ahmad met again at the starting point after 1 h, Will had completed 2.4 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Nick's distance : Ahmad's distance
2 : 6 - 2
2 : 4

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

Nick	Ahmad	Will
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Nick's rounds : Ahmad's rounds : Will's rounds
4 : 8 : 2

Distance that Will completed in 1 h = 2.4 km

2 rounds = 2.4 km = 2400 m

1 round = 2400 ÷ 2 = 1200 m

Circumference of the circular track = 1200 m

Answer(s): (a) 10; (b) 1200 m