Asher, Billy and Luis started walking at the same time from the same starting point round a circular track. Luis walked in the clockwise direction. Asher and Billy walked in an anti-clockwise direction. Luis took 12 min to complete each round. He met Asher after every 2 minutes. He met Billy after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Luis complete in 1 h?
- When Luis and Asher met again at the starting point after 1 h, Billy had completed 1.8 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Luis completed in 1 h
= 60 ÷ 12
= 5
(b)
Luis took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Luis's distance is the repeated identity.
Make Luis's distance the same.
Luis's distance : Asher's distance
2 : 12 - 2
2 : 10
Luis's distance : Billy's distance
4 : 12 - 4
4 : 8
Luis |
Asher |
Billy |
2x2 |
10x2 |
|
4x1 |
|
8x1 |
4 |
20 |
8 |
The distance of Luis is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
Luis's rounds : Asher's rounds : Billy's rounds
4 : 20 : 8
Distance that Billy completed in 1 h = 1.8 km
8 rounds = 1.8 km = 1800 m
1 round = 1800 ÷ 8 = 225 m
Circumference of the circular track = 225 m
Answer(s): (a) 5; (b) 225 m