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

1. How many rounds did Valen complete in 1 h?
2. When Valen and Pierre met again at the starting point after 1 h, Sam had completed 2.1 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Valen's distance : Pierre's distance
2 : 12 - 2
2 : 10

Valen's distance : Sam's distance
7 : 12 - 7
7 : 5

Valen	Pierre	Sam
2x7	10x7
7x2		5x2
14	70	10

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

In 1 h
Valen's rounds : Pierre's rounds : Sam's rounds
14 : 70 : 10

Distance that Sam completed in 1 h = 2.1 km

10 rounds = 2.1 km = 2100 m

1 round = 2100 ÷ 10 = 210 m

Circumference of the circular track = 210 m

Answer(s): (a) 5; (b) 210 m