Vincent, Ben and Jack started walking at the same time from the same starting point round a circular track. Jack walked in the clockwise direction. Vincent and Ben walked in an anti-clockwise direction. Jack took 5 min to complete each round. He met Vincent after every 3 minutes. He met Ben after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Jack complete in 1 h?
- When Jack and Vincent met again at the starting point after 1 h, Ben had completed 2.7 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 ÷ 5
= 12
(b)
Jack took 5 min to complete 1 round
1 min =
15 of circular track = 1 u
5 min =
55 of circular track = 5 u
Jack's distance is the repeated identity.
Make Jack's distance the same.
Jack's distance : Vincent's distance
3 : 5 - 3
3 : 2
Jack's distance : Ben's distance
4 : 5 - 4
4 : 1
Jack |
Vincent |
Ben |
3x4 |
2x4 |
|
4x3 |
|
1x3 |
12 |
8 |
3 |
The distance of Jack is the repeated identity.
LCM of 3 and 4 = 12
In 1 h
Jack's rounds : Vincent's rounds : Ben's rounds
12 : 8 : 3
Distance that Ben completed in 1 h = 2.7 km
3 rounds = 2.7 km = 2700 m
1 round = 2700 ÷ 3 = 900 m
Circumference of the circular track = 900 m
Answer(s): (a) 12; (b) 900 m