Vincent, Owen and Luke started walking at the same time from the same starting point round a circular track. Luke walked in the clockwise direction. Vincent and Owen walked in an anti-clockwise direction. Luke took 6 min to complete each round. He met Vincent after every 3 minutes. He met Owen after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Luke complete in 1 h?
2. When Luke and Vincent met again at the starting point after 1 h, Owen had completed 2.4 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Luke's distance : Vincent's distance
3 : 6 - 3
3 : 3

Luke's distance : Owen's distance
5 : 6 - 5
5 : 1

Luke	Vincent	Owen
3x5	3x5
5x3		1x3
15	15	3

The distance of Luke is the repeated identity. 
LCM of 3 and 5 = 15

In 1 h
Luke's rounds : Vincent's rounds : Owen's rounds
15 : 15 : 3

Distance that Owen completed in 1 h = 2.4 km

3 rounds = 2.4 km = 2400 m

1 round = 2400 ÷ 3 = 800 m

Circumference of the circular track = 800 m

Answer(s): (a) 10; (b) 800 m