Riordan, Peter and Ben started walking at the same time from the same starting point round a circular track. Ben walked in the clockwise direction. Riordan and Peter walked in an anti-clockwise direction. Ben took 12 min to complete each round. He met Riordan after every 2 minutes. He met Peter after every 7 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Ben complete in 1 h?
2. When Ben and Riordan met again at the starting point after 1 h, Peter had completed 2.5 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Ben's distance : Riordan's distance
2 : 12 - 2
2 : 10

Ben's distance : Peter's distance
7 : 12 - 7
7 : 5

Ben	Riordan	Peter
2x7	10x7
7x2		5x2
14	70	10

The distance of Ben is the repeated identity. 
LCM of 2 and 7 = 14

In 1 h
Ben's rounds : Riordan's rounds : Peter's rounds
14 : 70 : 10

Distance that Peter completed in 1 h = 2.5 km

10 rounds = 2.5 km = 2500 m

1 round = 2500 ÷ 10 = 250 m

Circumference of the circular track = 250 m

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