Michael, Henry and Archie started walking at the same time from the same starting point round a circular track. Archie walked in the clockwise direction. Michael and Henry walked in an anti-clockwise direction. Archie took 5 min to complete each round. He met Michael after every 3 minutes. He met Henry after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Archie complete in 1 h?
2. When Archie and Michael met again at the starting point after 1 h, Henry had completed 1.8 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

Number of rounds that Archie completed in 1 h
= 60 ÷ 5
= 12

(b)
Archie took 5 min to complete 1 round
1 min = ¹₅ of circular track = 1 u
5 min = ⁵₅ of circular track = 5 u

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

Archie's distance : Michael's distance
3 : 5 - 3
3 : 2

Archie's distance : Henry's distance
4 : 5 - 4
4 : 1

Archie	Michael	Henry
3x4	2x4
4x3		1x3
12	8	3

The distance of Archie is the repeated identity. 
LCM of 3 and 4 = 12

In 1 h
Archie's rounds : Michael's rounds : Henry's rounds
12 : 8 : 3

Distance that Henry completed in 1 h = 1.8 km

3 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 3 = 600 m

Circumference of the circular track = 600 m

Answer(s): (a) 12; (b) 600 m