Peter, Warren and Michael started walking at the same time from the same starting point round a circular track. Michael walked in the clockwise direction. Peter and Warren walked in an anti-clockwise direction. Michael took 5 min to complete each round. He met Peter after every 3 minutes. He met Warren after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Michael complete in 1 h?
- When Michael and Peter met again at the starting point after 1 h, Warren had completed 1.2 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Michael completed in 1 h
= 60 ÷ 5
= 12
(b)
Michael took 5 min to complete 1 round
1 min =
15 of circular track = 1 u
5 min =
55 of circular track = 5 u
Michael's distance is the repeated identity.
Make Michael's distance the same.
Michael's distance : Peter's distance
3 : 5 - 3
3 : 2
Michael's distance : Warren's distance
4 : 5 - 4
4 : 1
Michael |
Peter |
Warren |
3x4 |
2x4 |
|
4x3 |
|
1x3 |
12 |
8 |
3 |
The distance of Michael is the repeated identity.
LCM of 3 and 4 = 12
In 1 h
Michael's rounds : Peter's rounds : Warren's rounds
12 : 8 : 3
Distance that Warren completed in 1 h = 1.2 km
3 rounds = 1.2 km = 1200 m
1 round = 1200 ÷ 3 = 400 m
Circumference of the circular track = 400 m
Answer(s): (a) 12; (b) 400 m