John, Howard and Ahmad started walking at the same time from the same starting point round a circular track. Ahmad walked in the clockwise direction. John and Howard walked in an anti-clockwise direction. Ahmad took 6 min to complete each round. He met John after every 3 minutes. He met Howard 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 John met again at the starting point after 1 h, Howard had completed 1.8 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 : John's distance
3 : 6 - 3
3 : 3

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

Ahmad	John	Howard
3x4	3x4
4x3		2x3
12	12	6

The distance of Ahmad is the repeated identity. 
LCM of 3 and 4 = 12

In 1 h
Ahmad's rounds : John's rounds : Howard's rounds
12 : 12 : 6

Distance that Howard completed in 1 h = 1.8 km

6 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 3 = 300 m

Circumference of the circular track = 300 m

Answer(s): (a) 10; (b) 300 m