Bobby, Sam and Reggie started walking at the same time from the same starting point round a circular track. Reggie walked in the clockwise direction. Bobby and Sam walked in an anti-clockwise direction. Reggie took 6 min to complete each round. He met Bobby after every 2 minutes. He met Sam after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

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

(a)
1 h = 60 min

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

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

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

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

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

Reggie	Bobby	Sam
2x2	4x2
4x1		2x1
4	8	2

The distance of Reggie is the repeated identity. 
LCM of 2 and 4 = 4

In 1 h
Reggie's rounds : Bobby's rounds : Sam's rounds
4 : 8 : 2

Distance that Sam completed in 1 h = 2.7 km

2 rounds = 2.7 km = 2700 m

1 round = 2700 ÷ 2 = 1350 m

Circumference of the circular track = 1350 m

Answer(s): (a) 10; (b) 1350 m