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