Peter, Dylan and Reggie started walking at the same time from the same starting point round a circular track. Reggie walked in the clockwise direction. Peter and Dylan walked in an anti-clockwise direction. Reggie took 6 min to complete each round. He met Peter after every 4 minutes. He met Dylan after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Reggie complete in 1 h?
2. When Reggie and Peter met again at the starting point after 1 h, Dylan had completed 1.6 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Reggie's distance : Peter's distance
4 : 6 - 4
4 : 2

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

Reggie	Peter	Dylan
4x5	2x5
5x4		1x4
20	10	4

The distance of Reggie is the repeated identity. 
LCM of 4 and 5 = 20

In 1 h
Reggie's rounds : Peter's rounds : Dylan's rounds
20 : 10 : 4

Distance that Dylan completed in 1 h = 1.6 km

4 rounds = 1.6 km = 1600 m

1 round = 1600 ÷ 4 = 400 m

Circumference of the circular track = 400 m

Answer(s): (a) 10; (b) 400 m