Howard, Owen and Ken started walking at the same time from the same starting point round a circular track. Ken walked in the clockwise direction. Howard and Owen walked in an anti-clockwise direction. Ken took 5 min to complete each round. He met Howard after every 3 minutes. He met Owen after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Ken complete in 1 h?
- When Ken and Howard met again at the starting point after 1 h, Owen had completed 2.7 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Ken completed in 1 h
= 60 ÷ 5
= 12
(b)
Ken took 5 min to complete 1 round
1 min =
15 of circular track = 1 u
5 min =
55 of circular track = 5 u
Ken's distance is the repeated identity.
Make Ken's distance the same.
Ken's distance : Howard's distance
3 : 5 - 3
3 : 2
Ken's distance : Owen's distance
4 : 5 - 4
4 : 1
Ken |
Howard |
Owen |
3x4 |
2x4 |
|
4x3 |
|
1x3 |
12 |
8 |
3 |
The distance of Ken is the repeated identity.
LCM of 3 and 4 = 12
In 1 h
Ken's rounds : Howard's rounds : Owen's rounds
12 : 8 : 3
Distance that Owen completed in 1 h = 2.7 km
3 rounds = 2.7 km = 2700 m
1 round = 2700 ÷ 3 = 900 m
Circumference of the circular track = 900 m
Answer(s): (a) 12; (b) 900 m