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

1. How many rounds did Gabriel complete in 1 h?
2. When Gabriel and Albert met again at the starting point after 1 h, Paul had completed 2.7 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

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

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

Gabriel's distance : Albert's distance
4 : 6 - 4
4 : 2

Gabriel's distance : Paul's distance
5 : 6 - 5
5 : 1

Gabriel	Albert	Paul
4x5	2x5
5x4		1x4
20	10	4

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

In 1 h
Gabriel's rounds : Albert's rounds : Paul's rounds
20 : 10 : 4

Distance that Paul completed in 1 h = 2.7 km

4 rounds = 2.7 km = 2700 m

1 round = 2700 ÷ 4 = 675 m

Circumference of the circular track = 675 m

Answer(s): (a) 10; (b) 675 m