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

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

(a)
1 h = 60 min

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

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

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

Tommy's distance : Jeremy's distance
2 : 12 - 2
2 : 10

Tommy's distance : Vincent's distance
7 : 12 - 7
7 : 5

Tommy	Jeremy	Vincent
2x7	10x7
7x2		5x2
14	70	10

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

In 1 h
Tommy's rounds : Jeremy's rounds : Vincent's rounds
14 : 70 : 10

Distance that Vincent 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