Jenson, Julian and Tom started walking at the same time from the same starting point round a circular track. Tom walked in the clockwise direction. Jenson and Julian walked in an anti-clockwise direction. Tom took 6 min to complete each round. He met Jenson after every 2 minutes. He met Julian after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Tom complete in 1 h?
2. When Tom and Jenson met again at the starting point after 1 h, Julian had completed 1.6 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

Number of rounds that Tom completed in 1 h
= 60 ÷ 6
= 10

(b)
Tom took 6 min to complete 1 round
1 min = ¹₆ of circular track = 1 u
6 min = ⁶₆ of circular track = 6 u

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

Tom's distance : Jenson's distance
2 : 6 - 2
2 : 4

Tom's distance : Julian's distance
5 : 6 - 5
5 : 1

Tom	Jenson	Julian
2x5	4x5
5x2		1x2
10	20	2

The distance of Tom is the repeated identity. 
LCM of 2 and 5 = 10

In 1 h
Tom's rounds : Jenson's rounds : Julian's rounds
10 : 20 : 2

Distance that Julian completed in 1 h = 1.6 km

2 rounds = 1.6 km = 1600 m

1 round = 1600 ÷ 2 = 800 m

Circumference of the circular track = 800 m

Answer(s): (a) 10; (b) 800 m