Henry, Michael and Lee started walking at the same time from the same starting point round a circular track. Lee walked in the clockwise direction. Henry and Michael walked in an anti-clockwise direction. Lee took 12 min to complete each round. He met Henry after every 2 minutes. He met Michael after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Lee complete in 1 h?
- When Lee and Henry met again at the starting point after 1 h, Michael had completed 2.6 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Lee completed in 1 h
= 60 ÷ 12
= 5
(b)
Lee took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Lee's distance is the repeated identity.
Make Lee's distance the same.
Lee's distance : Henry's distance
2 : 12 - 2
2 : 10
Lee's distance : Michael's distance
4 : 12 - 4
4 : 8
Lee |
Henry |
Michael |
2x2 |
10x2 |
|
4x1 |
|
8x1 |
4 |
20 |
8 |
The distance of Lee is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
Lee's rounds : Henry's rounds : Michael's rounds
4 : 20 : 8
Distance that Michael completed in 1 h = 2.6 km
8 rounds = 2.6 km = 2600 m
1 round = 2600 ÷ 8 = 325 m
Circumference of the circular track = 325 m
Answer(s): (a) 5; (b) 325 m