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

1. How many rounds did Peter complete in 1 h?
2. When Peter and Oliver met again at the starting point after 1 h, Michael had completed 1.3 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Peter's distance : Oliver's distance
4 : 6 - 4
4 : 2

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

Peter	Oliver	Michael
4x5	2x5
5x4		1x4
20	10	4

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

In 1 h
Peter's rounds : Oliver's rounds : Michael's rounds
20 : 10 : 4

Distance that Michael completed in 1 h = 1.3 km

4 rounds = 1.3 km = 1300 m

1 round = 1300 ÷ 4 = 325 m

Circumference of the circular track = 325 m

Answer(s): (a) 10; (b) 325 m