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

1. How many rounds did Ahmad complete in 1 h?
2. When Ahmad and David met again at the starting point after 1 h, Tom had completed 2.1 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

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

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

Ahmad	David	Tom
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Ahmad's rounds : David's rounds : Tom's rounds
4 : 8 : 2

Distance that Tom completed in 1 h = 2.1 km

2 rounds = 2.1 km = 2100 m

1 round = 2100 ÷ 2 = 1050 m

Circumference of the circular track = 1050 m

Answer(s): (a) 10; (b) 1050 m