Charlie, Ian and Dylan started walking at the same time from the same starting point round a circular track. Dylan walked in the clockwise direction. Charlie and Ian walked in an anti-clockwise direction. Dylan took 6 min to complete each round. He met Charlie after every 2 minutes. He met Ian after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Dylan complete in 1 h?
- When Dylan and Charlie met again at the starting point after 1 h, Ian had completed 1.3 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Dylan completed in 1 h
= 60 ÷ 6
= 10
(b)
Dylan took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Dylan's distance is the repeated identity.
Make Dylan's distance the same.
Dylan's distance : Charlie's distance
2 : 6 - 2
2 : 4
Dylan's distance : Ian's distance
5 : 6 - 5
5 : 1
Dylan |
Charlie |
Ian |
2x5 |
4x5 |
|
5x2 |
|
1x2 |
10 |
20 |
2 |
The distance of Dylan is the repeated identity.
LCM of 2 and 5 = 10
In 1 h
Dylan's rounds : Charlie's rounds : Ian's rounds
10 : 20 : 2
Distance that Ian completed in 1 h = 1.3 km
2 rounds = 1.3 km = 1300 m
1 round = 1300 ÷ 2 = 650 m
Circumference of the circular track = 650 m
Answer(s): (a) 10; (b) 650 m