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

1. How many rounds did Bobby complete in 1 h?
2. When Bobby and Paul met again at the starting point after 1 h, Seth had completed 1.5 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

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

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

Bobby	Paul	Seth
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Bobby's rounds : Paul's rounds : Seth's rounds
4 : 8 : 2

Distance that Seth completed in 1 h = 1.5 km

2 rounds = 1.5 km = 1500 m

1 round = 1500 ÷ 2 = 750 m

Circumference of the circular track = 750 m

Answer(s): (a) 10; (b) 750 m