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

1. How many rounds did Fabian complete in 1 h?
2. When Fabian and Howard met again at the starting point after 1 h, Daniel had completed 1.7 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Fabian's distance : Howard's distance
2 : 6 - 2
2 : 4

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

Fabian	Howard	Daniel
2x2	4x2
4x1		2x1
4	8	2

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

In 1 h
Fabian's rounds : Howard's rounds : Daniel's rounds
4 : 8 : 2

Distance that Daniel completed in 1 h = 1.7 km

2 rounds = 1.7 km = 1700 m

1 round = 1700 ÷ 2 = 850 m

Circumference of the circular track = 850 m

Answer(s): (a) 10; (b) 850 m