Fabian, Ben and Jack started walking at the same time from the same starting point round a circular track. Jack walked in the clockwise direction. Fabian and Ben walked in an anti-clockwise direction. Jack took 12 min to complete each round. He met Fabian after every 3 minutes. He met Ben after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Jack complete in 1 h?
- When Jack and Fabian met again at the starting point after 1 h, Ben had completed 2.1 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Jack completed in 1 h
= 60 ÷ 12
= 5
(b)
Jack took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Jack's distance is the repeated identity.
Make Jack's distance the same.
Jack's distance : Fabian's distance
3 : 12 - 3
3 : 9
Jack's distance : Ben's distance
6 : 12 - 6
6 : 6
Jack |
Fabian |
Ben |
3x2 |
9x2 |
|
6x1 |
|
6x1 |
6 |
18 |
6 |
The distance of Jack is the repeated identity.
LCM of 3 and 6 = 6
In 1 h
Jack's rounds : Fabian's rounds : Ben's rounds
6 : 18 : 6
Distance that Ben completed in 1 h = 2.1 km
6 rounds = 2.1 km = 2100 m
1 round = 2100 ÷ 6 = 350 m
Circumference of the circular track = 350 m
Answer(s): (a) 5; (b) 350 m