Lee, Zeph and Jeremy started walking at the same time from the same starting point round a circular track. Jeremy walked in the clockwise direction. Lee and Zeph walked in an anti-clockwise direction. Jeremy took 12 min to complete each round. He met Lee after every 2 minutes. He met Zeph after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Jeremy complete in 1 h?
- When Jeremy and Lee met again at the starting point after 1 h, Zeph had completed 1.8 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Jeremy completed in 1 h
= 60 ÷ 12
= 5
(b)
Jeremy took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Jeremy's distance is the repeated identity.
Make Jeremy's distance the same.
Jeremy's distance : Lee's distance
2 : 12 - 2
2 : 10
Jeremy's distance : Zeph's distance
4 : 12 - 4
4 : 8
Jeremy |
Lee |
Zeph |
2x2 |
10x2 |
|
4x1 |
|
8x1 |
4 |
20 |
8 |
The distance of Jeremy is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
Jeremy's rounds : Lee's rounds : Zeph's rounds
4 : 20 : 8
Distance that Zeph completed in 1 h = 1.8 km
8 rounds = 1.8 km = 1800 m
1 round = 1800 ÷ 8 = 225 m
Circumference of the circular track = 225 m
Answer(s): (a) 5; (b) 225 m