Tom, Pierre and Tim started walking at the same time from the same starting point round a circular track. Tim walked in the clockwise direction. Tom and Pierre walked in an anti-clockwise direction. Tim took 12 min to complete each round. He met Tom after every 2 minutes. He met Pierre after every 6 minutes. The three friends kept to their respective speeds throughout their walk.

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

(a)
1 h = 60 min

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

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

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

Tim's distance : Tom's distance
2 : 12 - 2
2 : 10

Tim's distance : Pierre's distance
6 : 12 - 6
6 : 6

Tim	Tom	Pierre
2x3	10x3
6x1		6x1
6	30	6

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

In 1 h
Tim's rounds : Tom's rounds : Pierre's rounds
6 : 30 : 6

Distance that Pierre completed in 1 h = 2.7 km

6 rounds = 2.7 km = 2700 m

1 round = 2700 ÷ 6 = 450 m

Circumference of the circular track = 450 m

Answer(s): (a) 5; (b) 450 m