Howard, Neave and Perry started walking at the same time from the same starting point round a circular track. Perry walked in the clockwise direction. Howard and Neave walked in an anti-clockwise direction. Perry took 6 min to complete each round. He met Howard after every 4 minutes. He met Neave after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Perry complete in 1 h?
2. When Perry and Howard met again at the starting point after 1 h, Neave had completed 1.4 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Perry's distance : Howard's distance
4 : 6 - 4
4 : 2

Perry's distance : Neave's distance
5 : 6 - 5
5 : 1

Perry	Howard	Neave
4x5	2x5
5x4		1x4
20	10	4

The distance of Perry is the repeated identity. 
LCM of 4 and 5 = 20

In 1 h
Perry's rounds : Howard's rounds : Neave's rounds
20 : 10 : 4

Distance that Neave completed in 1 h = 1.4 km

4 rounds = 1.4 km = 1400 m

1 round = 1400 ÷ 4 = 350 m

Circumference of the circular track = 350 m

Answer(s): (a) 10; (b) 350 m