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

1. How many rounds did Riordan complete in 1 h?
2. When Riordan and Asher met again at the starting point after 1 h, Perry had completed 1.5 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Riordan's distance : Asher's distance
3 : 6 - 3
3 : 3

Riordan's distance : Perry's distance
5 : 6 - 5
5 : 1

Riordan	Asher	Perry
3x5	3x5
5x3		1x3
15	15	3

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

In 1 h
Riordan's rounds : Asher's rounds : Perry's rounds
15 : 15 : 3

Distance that Perry completed in 1 h = 1.5 km

3 rounds = 1.5 km = 1500 m

1 round = 1500 ÷ 3 = 500 m

Circumference of the circular track = 500 m

Answer(s): (a) 10; (b) 500 m