Riordan, Billy and Ahmad started walking at the same time from the same starting point round a circular track. Ahmad walked in the clockwise direction. Riordan and Billy walked in an anti-clockwise direction. Ahmad took 12 min to complete each round. He met Riordan after every 2 minutes. He met Billy 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 Riordan met again at the starting point after 1 h, Billy had completed 2.2 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 ÷ 12
= 5

(b)
Ahmad took 12 min to complete 1 round
1 min = ¹₁₂ of circular track = 1 u
12 min = ¹²₁₂ of circular track = 12 u

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

Ahmad's distance : Riordan's distance
2 : 12 - 2
2 : 10

Ahmad's distance : Billy's distance
4 : 12 - 4
4 : 8

Ahmad	Riordan	Billy
2x2	10x2
4x1		8x1
4	20	8

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

In 1 h
Ahmad's rounds : Riordan's rounds : Billy's rounds
4 : 20 : 8

Distance that Billy completed in 1 h = 2.2 km

8 rounds = 2.2 km = 2200 m

1 round = 2200 ÷ 8 = 275 m

Circumference of the circular track = 275 m

Answer(s): (a) 5; (b) 275 m