Pierre, Simon and Harry started walking at the same time from the same starting point round a circular track. Harry walked in the clockwise direction. Pierre and Simon walked in an anti-clockwise direction. Harry took 5 min to complete each round. He met Pierre after every 3 minutes. He met Simon after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Harry complete in 1 h?
2. When Harry and Pierre met again at the starting point after 1 h, Simon had completed 1.2 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

(b)
Harry took 5 min to complete 1 round
1 min = ¹₅ of circular track = 1 u
5 min = ⁵₅ of circular track = 5 u

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

Harry's distance : Pierre's distance
3 : 5 - 3
3 : 2

Harry's distance : Simon's distance
4 : 5 - 4
4 : 1

Harry	Pierre	Simon
3x4	2x4
4x3		1x3
12	8	3

The distance of Harry is the repeated identity. 
LCM of 3 and 4 = 12

In 1 h
Harry's rounds : Pierre's rounds : Simon's rounds
12 : 8 : 3

Distance that Simon completed in 1 h = 1.2 km

3 rounds = 1.2 km = 1200 m

1 round = 1200 ÷ 3 = 400 m

Circumference of the circular track = 400 m

Answer(s): (a) 12; (b) 400 m