Tom, Henry and Luis started walking at the same time from the same starting point round a circular track. Luis walked in the clockwise direction. Tom and Henry walked in an anti-clockwise direction. Luis took 5 min to complete each round. He met Tom after every 3 minutes. He met Henry 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 Tom met again at the starting point after 1 h, Henry 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 ÷ 5
= 12
(b)
Luis took 5 min to complete 1 round
1 min =
15 of circular track = 1 u
5 min =
55 of circular track = 5 u
Luis's distance is the repeated identity.
Make Luis's distance the same.
Luis's distance : Tom's distance
3 : 5 - 3
3 : 2
Luis's distance : Henry's distance
4 : 5 - 4
4 : 1
Luis |
Tom |
Henry |
3x4 |
2x4 |
|
4x3 |
|
1x3 |
12 |
8 |
3 |
The distance of Luis is the repeated identity.
LCM of 3 and 4 = 12
In 1 h
Luis's rounds : Tom's rounds : Henry's rounds
12 : 8 : 3
Distance that Henry 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