Michael, Charlie and Fred started walking at the same time from the same starting point round a circular track. Fred walked in the clockwise direction. Michael and Charlie walked in an anti-clockwise direction. Fred took 6 min to complete each round. He met Michael after every 2 minutes. He met Charlie after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Fred complete in 1 h?
2. When Fred and Michael met again at the starting point after 1 h, Charlie had completed 1.3 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Fred's distance : Michael's distance
2 : 6 - 2
2 : 4

Fred's distance : Charlie's distance
4 : 6 - 4
4 : 2

Fred	Michael	Charlie
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Fred's rounds : Michael's rounds : Charlie's rounds
4 : 8 : 2

Distance that Charlie completed in 1 h = 1.3 km

2 rounds = 1.3 km = 1300 m

1 round = 1300 ÷ 2 = 650 m

Circumference of the circular track = 650 m

Answer(s): (a) 10; (b) 650 m