Fabian, Bobby and Brandon started walking at the same time from the same starting point round a circular track. Brandon walked in the clockwise direction. Fabian and Bobby walked in an anti-clockwise direction. Brandon took 12 min to complete each round. He met Fabian after every 2 minutes. He met Bobby after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Brandon complete in 1 h?
- When Brandon and Fabian met again at the starting point after 1 h, Bobby had completed 1.8 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Brandon completed in 1 h
= 60 ÷ 12
= 5
(b)
Brandon took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Brandon's distance is the repeated identity.
Make Brandon's distance the same.
Brandon's distance : Fabian's distance
2 : 12 - 2
2 : 10
Brandon's distance : Bobby's distance
6 : 12 - 6
6 : 6
Brandon |
Fabian |
Bobby |
2x3 |
10x3 |
|
6x1 |
|
6x1 |
6 |
30 |
6 |
The distance of Brandon is the repeated identity.
LCM of 2 and 6 = 6
In 1 h
Brandon's rounds : Fabian's rounds : Bobby's rounds
6 : 30 : 6
Distance that Bobby completed in 1 h = 1.8 km
6 rounds = 1.8 km = 1800 m
1 round = 1800 ÷ 6 = 300 m
Circumference of the circular track = 300 m
Answer(s): (a) 5; (b) 300 m