Glen, Vincent and Elijah started walking at the same time from the same starting point round a circular track. Elijah walked in the clockwise direction. Glen and Vincent walked in an anti-clockwise direction. Elijah took 6 min to complete each round. He met Glen after every 4 minutes. He met Vincent after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Elijah complete in 1 h?
- When Elijah and Glen met again at the starting point after 1 h, Vincent had completed 2.1 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Elijah completed in 1 h
= 60 ÷ 6
= 10
(b)
Elijah took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Elijah's distance is the repeated identity.
Make Elijah's distance the same.
Elijah's distance : Glen's distance
4 : 6 - 4
4 : 2
Elijah's distance : Vincent's distance
5 : 6 - 5
5 : 1
Elijah |
Glen |
Vincent |
4x5 |
2x5 |
|
5x4 |
|
1x4 |
20 |
10 |
4 |
The distance of Elijah is the repeated identity.
LCM of 4 and 5 = 20
In 1 h
Elijah's rounds : Glen's rounds : Vincent's rounds
20 : 10 : 4
Distance that Vincent completed in 1 h = 2.1 km
4 rounds = 2.1 km = 2100 m
1 round = 2100 ÷ 4 = 525 m
Circumference of the circular track = 525 m
Answer(s): (a) 10; (b) 525 m