Reggie, Lee and Billy started walking at the same time from the same starting point round a circular track. Billy walked in the clockwise direction. Reggie and Lee walked in an anti-clockwise direction. Billy took 6 min to complete each round. He met Reggie after every 2 minutes. He met Lee after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Billy complete in 1 h?
2. When Billy and Reggie met again at the starting point after 1 h, Lee had completed 2.2 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Billy's distance : Reggie's distance
2 : 6 - 2
2 : 4

Billy's distance : Lee's distance
5 : 6 - 5
5 : 1

Billy	Reggie	Lee
2x5	4x5
5x2		1x2
10	20	2

The distance of Billy is the repeated identity. 
LCM of 2 and 5 = 10

In 1 h
Billy's rounds : Reggie's rounds : Lee's rounds
10 : 20 : 2

Distance that Lee completed in 1 h = 2.2 km

2 rounds = 2.2 km = 2200 m

1 round = 2200 ÷ 2 = 1100 m

Circumference of the circular track = 1100 m

Answer(s): (a) 10; (b) 1100 m