Reggie, Jack and Eric started walking at the same time from the same starting point round a circular track. Eric walked in the clockwise direction. Reggie and Jack walked in an anti-clockwise direction. Eric took 12 min to complete each round. He met Reggie after every 2 minutes. He met Jack after every 4 minutes. The three friends kept to their respective speeds throughout their walk.

1. How many rounds did Eric complete in 1 h?
2. When Eric and Reggie met again at the starting point after 1 h, Jack had completed 2.8 km. Find the circumference of the circular track in metres.

(a)
1 h = 60 min

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

(b)
Eric took 12 min to complete 1 round
1 min = ¹₁₂ of circular track = 1 u
12 min = ¹²₁₂ of circular track = 12 u

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

Eric's distance : Reggie's distance
2 : 12 - 2
2 : 10

Eric's distance : Jack's distance
4 : 12 - 4
4 : 8

Eric	Reggie	Jack
2x2	10x2
4x1		8x1
4	20	8

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

In 1 h
Eric's rounds : Reggie's rounds : Jack's rounds
4 : 20 : 8

Distance that Jack completed in 1 h = 2.8 km

8 rounds = 2.8 km = 2800 m

1 round = 2800 ÷ 8 = 350 m

Circumference of the circular track = 350 m

Answer(s): (a) 5; (b) 350 m