Ben, Ivan and Fred started walking at the same time from the same starting point round a circular track. Fred walked in the clockwise direction. Ben and Ivan walked in an anti-clockwise direction. Fred took 5 min to complete each round. He met Ben after every 3 minutes. He met Ivan after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Fred complete in 1 h?
2. When Fred and Ben met again at the starting point after 1 h, Ivan had completed 1.8 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

Number of rounds that Fred completed in 1 h
= 60 ÷ 5
= 12

(b)
Fred took 5 min to complete 1 round
1 min = ¹₅ of circular track = 1 u
5 min = ⁵₅ of circular track = 5 u

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

Fred's distance : Ben's distance
3 : 5 - 3
3 : 2

Fred's distance : Ivan's distance
4 : 5 - 4
4 : 1

Fred	Ben	Ivan
3x4	2x4
4x3		1x3
12	8	3

The distance of Fred is the repeated identity. 
LCM of 3 and 4 = 12

In 1 h
Fred's rounds : Ben's rounds : Ivan's rounds
12 : 8 : 3

Distance that Ivan completed in 1 h = 1.8 km

3 rounds = 1.8 km = 1800 m

1 round = 1800 ÷ 3 = 600 m

Circumference of the circular track = 600 m

Answer(s): (a) 12; (b) 600 m