Ken, Ian and Seth started walking at the same time from the same starting point round a circular track. Seth walked in the clockwise direction. Ken and Ian walked in an anti-clockwise direction. Seth took 6 min to complete each round. He met Ken after every 3 minutes. He met Ian after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Seth complete in 1 h?
- When Seth and Ken met again at the starting point after 1 h, Ian had completed 1.5 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Seth completed in 1 h
= 60 ÷ 6
= 10
(b)
Seth took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Seth's distance is the repeated identity.
Make Seth's distance the same.
Seth's distance : Ken's distance
3 : 6 - 3
3 : 3
Seth's distance : Ian's distance
5 : 6 - 5
5 : 1
Seth |
Ken |
Ian |
3x5 |
3x5 |
|
5x3 |
|
1x3 |
15 |
15 |
3 |
The distance of Seth is the repeated identity.
LCM of 3 and 5 = 15
In 1 h
Seth's rounds : Ken's rounds : Ian's rounds
15 : 15 : 3
Distance that Ian completed in 1 h = 1.5 km
3 rounds = 1.5 km = 1500 m
1 round = 1500 ÷ 3 = 500 m
Circumference of the circular track = 500 m
Answer(s): (a) 10; (b) 500 m