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

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

(a)
1 h = 60 min

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

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

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

Warren's distance : Oscar's distance
2 : 6 - 2
2 : 4

Warren's distance : Brandon's distance
5 : 6 - 5
5 : 1

Warren	Oscar	Brandon
2x5	4x5
5x2		1x2
10	20	2

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

In 1 h
Warren's rounds : Oscar's rounds : Brandon's rounds
10 : 20 : 2

Distance that Brandon 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