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

1. How many rounds did Jenson complete in 1 h?
2. When Jenson and Peter met again at the starting point after 1 h, Nick had completed 2.7 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Jenson's distance : Peter's distance
2 : 12 - 2
2 : 10

Jenson's distance : Nick's distance
7 : 12 - 7
7 : 5

Jenson	Peter	Nick
2x7	10x7
7x2		5x2
14	70	10

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

In 1 h
Jenson's rounds : Peter's rounds : Nick's rounds
14 : 70 : 10

Distance that Nick completed in 1 h = 2.7 km

10 rounds = 2.7 km = 2700 m

1 round = 2700 ÷ 10 = 270 m

Circumference of the circular track = 270 m

Answer(s): (a) 5; (b) 270 m