Ethan, Paul and Riordan started walking at the same time from the same starting point round a circular track. Riordan walked in the clockwise direction. Ethan and Paul walked in an anti-clockwise direction. Riordan took 6 min to complete each round. He met Ethan after every 2 minutes. He met Paul after every 4 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 Ethan met again at the starting point after 1 h, Paul had completed 1.8 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 : Ethan's distance
2 : 6 - 2
2 : 4

Riordan's distance : Paul's distance
4 : 6 - 4
4 : 2

Riordan	Ethan	Paul
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Riordan's rounds : Ethan's rounds : Paul's rounds
4 : 8 : 2

Distance that Paul completed in 1 h = 1.8 km

2 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 2 = 900 m

Circumference of the circular track = 900 m

Answer(s): (a) 10; (b) 900 m