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

1. How many rounds did Japheth complete in 1 h?
2. When Japheth and Pierre met again at the starting point after 1 h, Peter had completed 2.4 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Japheth's distance : Pierre's distance
2 : 6 - 2
2 : 4

Japheth's distance : Peter's distance
5 : 6 - 5
5 : 1

Japheth	Pierre	Peter
2x5	4x5
5x2		1x2
10	20	2

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

In 1 h
Japheth's rounds : Pierre's rounds : Peter's rounds
10 : 20 : 2

Distance that Peter completed in 1 h = 2.4 km

2 rounds = 2.4 km = 2400 m

1 round = 2400 ÷ 2 = 1200 m

Circumference of the circular track = 1200 m

Answer(s): (a) 10; (b) 1200 m