Ahmad, Michael and Seth started walking at the same time from the same starting point round a circular track. Seth walked in the clockwise direction. Ahmad and Michael walked in an anti-clockwise direction. Seth took 6 min to complete each round. He met Ahmad after every 2 minutes. He met Michael 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 Ahmad 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 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 : Ahmad's distance
2 : 6 - 2
2 : 4
Seth's distance : Michael's distance
5 : 6 - 5
5 : 1
Seth |
Ahmad |
Michael |
2x5 |
4x5 |
|
5x2 |
|
1x2 |
10 |
20 |
2 |
The distance of Seth is the repeated identity.
LCM of 2 and 5 = 10
In 1 h
Seth's rounds : Ahmad's rounds : Michael's rounds
10 : 20 : 2
Distance that Michael completed in 1 h = 2.6 km
2 rounds = 2.6 km = 2600 m
1 round = 2600 ÷ 2 = 1300 m
Circumference of the circular track = 1300 m
Answer(s): (a) 10; (b) 1300 m