Zane, Vaidev and Henry started walking at the same time from the same starting point round a circular track. Henry walked in the clockwise direction. Zane and Vaidev walked in an anti-clockwise direction. Henry took 6 min to complete each round. He met Zane after every 4 minutes. He met Vaidev after every 5 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Henry complete in 1 h?
2. When Henry and Zane met again at the starting point after 1 h, Vaidev had completed 2.6 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Henry's distance : Zane's distance
4 : 6 - 4
4 : 2

Henry's distance : Vaidev's distance
5 : 6 - 5
5 : 1

Henry	Zane	Vaidev
4x5	2x5
5x4		1x4
20	10	4

The distance of Henry is the repeated identity. 
LCM of 4 and 5 = 20

In 1 h
Henry's rounds : Zane's rounds : Vaidev's rounds
20 : 10 : 4

Distance that Vaidev completed in 1 h = 2.6 km

4 rounds = 2.6 km = 2600 m

1 round = 2600 ÷ 4 = 650 m

Circumference of the circular track = 650 m

Answer(s): (a) 10; (b) 650 m