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

1. How many rounds did Daniel complete in 1 h?
2. When Daniel and Luis met again at the starting point after 1 h, John had completed 2.9 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Daniel's distance : Luis's distance
2 : 6 - 2
2 : 4

Daniel's distance : John's distance
5 : 6 - 5
5 : 1

Daniel	Luis	John
2x5	4x5
5x2		1x2
10	20	2

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

In 1 h
Daniel's rounds : Luis's rounds : John's rounds
10 : 20 : 2

Distance that John completed in 1 h = 2.9 km

2 rounds = 2.9 km = 2900 m

1 round = 2900 ÷ 2 = 1450 m

Circumference of the circular track = 1450 m

Answer(s): (a) 10; (b) 1450 m