Bryan, Daniel and Peter started walking at the same time from the same starting point round a circular track. Peter walked in the clockwise direction. Bryan and Daniel walked in an anti-clockwise direction. Peter took 12 min to complete each round. He met Bryan after every 2 minutes. He met Daniel after every 6 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 Bryan met again at the starting point after 1 h, Daniel had completed 1.5 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 ÷ 12
= 5

(b)
Peter took 12 min to complete 1 round
1 min = ¹₁₂ of circular track = 1 u
12 min = ¹²₁₂ of circular track = 12 u

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

Peter's distance : Bryan's distance
2 : 12 - 2
2 : 10

Peter's distance : Daniel's distance
6 : 12 - 6
6 : 6

Peter	Bryan	Daniel
2x3	10x3
6x1		6x1
6	30	6

The distance of Peter is the repeated identity. 
LCM of 2 and 6 = 6

In 1 h
Peter's rounds : Bryan's rounds : Daniel's rounds
6 : 30 : 6

Distance that Daniel completed in 1 h = 1.5 km

6 rounds = 1.5 km = 1500 m

1 round = 1500 ÷ 6 = 250 m

Circumference of the circular track = 250 m

Answer(s): (a) 5; (b) 250 m