Luke, Mark and Neave started walking at the same time from the same starting point round a circular track. Neave walked in the clockwise direction. Luke and Mark walked in an anti-clockwise direction. Neave took 12 min to complete each round. He met Luke after every 2 minutes. He met Mark after every 7 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Neave complete in 1 h?
2. When Neave and Luke met again at the starting point after 1 h, Mark had completed 2.2 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Neave's distance : Luke's distance
2 : 12 - 2
2 : 10

Neave's distance : Mark's distance
7 : 12 - 7
7 : 5

Neave	Luke	Mark
2x7	10x7
7x2		5x2
14	70	10

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

In 1 h
Neave's rounds : Luke's rounds : Mark's rounds
14 : 70 : 10

Distance that Mark completed in 1 h = 2.2 km

10 rounds = 2.2 km = 2200 m

1 round = 2200 ÷ 10 = 220 m

Circumference of the circular track = 220 m

Answer(s): (a) 5; (b) 220 m