Ben, Zane and Perry started walking at the same time from the same starting point round a circular track. Perry walked in the clockwise direction. Ben and Zane walked in an anti-clockwise direction. Perry took 12 min to complete each round. He met Ben after every 2 minutes. He met Zane after every 7 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Perry complete in 1 h?
- When Perry and Ben met again at the starting point after 1 h, Zane had completed 2.3 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Perry completed in 1 h
= 60 ÷ 12
= 5
(b)
Perry took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Perry's distance is the repeated identity.
Make Perry's distance the same.
Perry's distance : Ben's distance
2 : 12 - 2
2 : 10
Perry's distance : Zane's distance
7 : 12 - 7
7 : 5
Perry |
Ben |
Zane |
2x7 |
10x7 |
|
7x2 |
|
5x2 |
14 |
70 |
10 |
The distance of Perry is the repeated identity.
LCM of 2 and 7 = 14
In 1 h
Perry's rounds : Ben's rounds : Zane's rounds
14 : 70 : 10
Distance that Zane completed in 1 h = 2.3 km
10 rounds = 2.3 km = 2300 m
1 round = 2300 ÷ 10 = 230 m
Circumference of the circular track = 230 m
Answer(s): (a) 5; (b) 230 m