Lee, Gabriel and John started walking at the same time from the same starting point round a circular track. John walked in the clockwise direction. Lee and Gabriel walked in an anti-clockwise direction. John took 12 min to complete each round. He met Lee after every 2 minutes. He met Gabriel after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did John complete in 1 h?
- When John and Lee met again at the starting point after 1 h, Gabriel had completed 1.8 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that John completed in 1 h
= 60 ÷ 12
= 5
(b)
John took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
John's distance is the repeated identity.
Make John's distance the same.
John's distance : Lee's distance
2 : 12 - 2
2 : 10
John's distance : Gabriel's distance
6 : 12 - 6
6 : 6
John |
Lee |
Gabriel |
2x3 |
10x3 |
|
6x1 |
|
6x1 |
6 |
30 |
6 |
The distance of John is the repeated identity.
LCM of 2 and 6 = 6
In 1 h
John's rounds : Lee's rounds : Gabriel's rounds
6 : 30 : 6
Distance that Gabriel completed in 1 h = 1.8 km
6 rounds = 1.8 km = 1800 m
1 round = 1800 ÷ 6 = 300 m
Circumference of the circular track = 300 m
Answer(s): (a) 5; (b) 300 m