Fabian, George and Dylan started walking at the same time from the same starting point round a circular track. Dylan walked in the clockwise direction. Fabian and George walked in an anti-clockwise direction. Dylan took 6 min to complete each round. He met Fabian after every 3 minutes. He met George after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Dylan complete in 1 h?
2. When Dylan and Fabian met again at the starting point after 1 h, George had completed 1.8 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Dylan's distance : Fabian's distance
3 : 6 - 3
3 : 3

Dylan's distance : George's distance
5 : 6 - 5
5 : 1

Dylan	Fabian	George
3x5	3x5
5x3		1x3
15	15	3

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

In 1 h
Dylan's rounds : Fabian's rounds : George's rounds
15 : 15 : 3

Distance that George completed in 1 h = 1.8 km

3 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 3 = 600 m

Circumference of the circular track = 600 m

Answer(s): (a) 10; (b) 600 m