Bryan, Albert and Howard started walking at the same time from the same starting point round a circular track. Howard walked in the clockwise direction. Bryan and Albert walked in an anti-clockwise direction. Howard took 12 min to complete each round. He met Bryan after every 4 minutes. He met Albert after every 6 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Howard complete in 1 h?
2. When Howard and Bryan met again at the starting point after 1 h, Albert had completed 2.7 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Howard's distance : Bryan's distance
4 : 12 - 4
4 : 8

Howard's distance : Albert's distance
6 : 12 - 6
6 : 6

Howard	Bryan	Albert
4x3	8x3
6x2		6x2
12	24	12

The distance of Howard is the repeated identity. 
LCM of 4 and 6 = 12

In 1 h
Howard's rounds : Bryan's rounds : Albert's rounds
12 : 24 : 12

Distance that Albert completed in 1 h = 2.7 km

12 rounds = 2.7 km = 2700 m

1 round = 2700 ÷ 12 = 225 m

Circumference of the circular track = 225 m

Answer(s): (a) 5; (b) 225 m