Pierre, Reggie and Elijah started walking at the same time from the same starting point round a circular track. Elijah walked in the clockwise direction. Pierre and Reggie walked in an anti-clockwise direction. Elijah took 12 min to complete each round. He met Pierre after every 3 minutes. He met Reggie after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Elijah complete in 1 h?
- When Elijah and Pierre met again at the starting point after 1 h, Reggie had completed 2.4 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 ÷ 12
= 5
(b)
Elijah took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Elijah's distance is the repeated identity.
Make Elijah's distance the same.
Elijah's distance : Pierre's distance
3 : 12 - 3
3 : 9
Elijah's distance : Reggie's distance
6 : 12 - 6
6 : 6
Elijah |
Pierre |
Reggie |
3x2 |
9x2 |
|
6x1 |
|
6x1 |
6 |
18 |
6 |
The distance of Elijah is the repeated identity.
LCM of 3 and 6 = 6
In 1 h
Elijah's rounds : Pierre's rounds : Reggie's rounds
6 : 18 : 6
Distance that Reggie completed in 1 h = 2.4 km
6 rounds = 2.4 km = 2400 m
1 round = 2400 ÷ 6 = 400 m
Circumference of the circular track = 400 m
Answer(s): (a) 5; (b) 400 m