Vaidev, Ben and Archie started walking at the same time from the same starting point round a circular track. Archie walked in the clockwise direction. Vaidev and Ben walked in an anti-clockwise direction. Archie took 12 min to complete each round. He met Vaidev after every 2 minutes. He met Ben after every 7 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 Vaidev met again at the starting point after 1 h, Ben had completed 2.9 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 ÷ 12
= 5

(b)
Archie took 12 min to complete 1 round
1 min = ¹₁₂ of circular track = 1 u
12 min = ¹²₁₂ of circular track = 12 u

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

Archie's distance : Vaidev's distance
2 : 12 - 2
2 : 10

Archie's distance : Ben's distance
7 : 12 - 7
7 : 5

Archie	Vaidev	Ben
2x7	10x7
7x2		5x2
14	70	10

The distance of Archie is the repeated identity. 
LCM of 2 and 7 = 14

In 1 h
Archie's rounds : Vaidev's rounds : Ben's rounds
14 : 70 : 10

Distance that Ben completed in 1 h = 2.9 km

10 rounds = 2.9 km = 2900 m

1 round = 2900 ÷ 10 = 290 m

Circumference of the circular track = 290 m

Answer(s): (a) 5; (b) 290 m