Eric, Flynn and Ryan started walking at the same time from the same starting point round a circular track. Ryan walked in the clockwise direction. Eric and Flynn walked in an anti-clockwise direction. Ryan took 6 min to complete each round. He met Eric after every 2 minutes. He met Flynn after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Ryan complete in 1 h?
2. When Ryan and Eric met again at the starting point after 1 h, Flynn had completed 2.5 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Ryan's distance : Eric's distance
2 : 6 - 2
2 : 4

Ryan's distance : Flynn's distance
5 : 6 - 5
5 : 1

Ryan	Eric	Flynn
2x5	4x5
5x2		1x2
10	20	2

The distance of Ryan is the repeated identity. 
LCM of 2 and 5 = 10

In 1 h
Ryan's rounds : Eric's rounds : Flynn's rounds
10 : 20 : 2

Distance that Flynn completed in 1 h = 2.5 km

2 rounds = 2.5 km = 2500 m

1 round = 2500 ÷ 2 = 1250 m

Circumference of the circular track = 1250 m

Answer(s): (a) 10; (b) 1250 m