Andy, Peter and John started walking at the same time from the same starting point round a circular track. John walked in the clockwise direction. Andy and Peter walked in an anti-clockwise direction. John took 5 min to complete each round. He met Andy after every 3 minutes. He met Peter after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did John complete in 1 h?
- When John and Andy met again at the starting point after 1 h, Peter had completed 2.1 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 ÷ 5
= 12
(b)
John took 5 min to complete 1 round
1 min =
15 of circular track = 1 u
5 min =
55 of circular track = 5 u
John's distance is the repeated identity.
Make John's distance the same.
John's distance : Andy's distance
3 : 5 - 3
3 : 2
John's distance : Peter's distance
4 : 5 - 4
4 : 1
John |
Andy |
Peter |
3x4 |
2x4 |
|
4x3 |
|
1x3 |
12 |
8 |
3 |
The distance of John is the repeated identity.
LCM of 3 and 4 = 12
In 1 h
John's rounds : Andy's rounds : Peter's rounds
12 : 8 : 3
Distance that Peter completed in 1 h = 2.1 km
3 rounds = 2.1 km = 2100 m
1 round = 2100 ÷ 3 = 700 m
Circumference of the circular track = 700 m
Answer(s): (a) 12; (b) 700 m