Ivan, Ethan and Bryan started walking at the same time from the same starting point round a circular track. Bryan walked in the clockwise direction. Ivan and Ethan walked in an anti-clockwise direction. Bryan took 12 min to complete each round. He met Ivan after every 2 minutes. He met Ethan after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Bryan complete in 1 h?
- When Bryan and Ivan met again at the starting point after 1 h, Ethan had completed 2.7 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Bryan completed in 1 h
= 60 ÷ 12
= 5
(b)
Bryan took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Bryan's distance is the repeated identity.
Make Bryan's distance the same.
Bryan's distance : Ivan's distance
2 : 12 - 2
2 : 10
Bryan's distance : Ethan's distance
6 : 12 - 6
6 : 6
Bryan |
Ivan |
Ethan |
2x3 |
10x3 |
|
6x1 |
|
6x1 |
6 |
30 |
6 |
The distance of Bryan is the repeated identity.
LCM of 2 and 6 = 6
In 1 h
Bryan's rounds : Ivan's rounds : Ethan's rounds
6 : 30 : 6
Distance that Ethan completed in 1 h = 2.7 km
6 rounds = 2.7 km = 2700 m
1 round = 2700 ÷ 6 = 450 m
Circumference of the circular track = 450 m
Answer(s): (a) 5; (b) 450 m