Cody, Luis and Pierre started walking at the same time from the same starting point round a circular track. Pierre walked in the clockwise direction. Cody and Luis walked in an anti-clockwise direction. Pierre took 12 min to complete each round. He met Cody after every 2 minutes. He met Luis after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Pierre complete in 1 h?
- When Pierre and Cody met again at the starting point after 1 h, Luis had completed 2.4 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Pierre completed in 1 h
= 60 ÷ 12
= 5
(b)
Pierre took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Pierre's distance is the repeated identity.
Make Pierre's distance the same.
Pierre's distance : Cody's distance
2 : 12 - 2
2 : 10
Pierre's distance : Luis's distance
6 : 12 - 6
6 : 6
Pierre |
Cody |
Luis |
2x3 |
10x3 |
|
6x1 |
|
6x1 |
6 |
30 |
6 |
The distance of Pierre is the repeated identity.
LCM of 2 and 6 = 6
In 1 h
Pierre's rounds : Cody's rounds : Luis's rounds
6 : 30 : 6
Distance that Luis 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