Ivan, Ahmad and John started walking at the same time from the same starting point round a circular track. John walked in the clockwise direction. Ivan and Ahmad walked in an anti-clockwise direction. John took 6 min to complete each round. He met Ivan after every 2 minutes. He met Ahmad 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 Ivan met again at the starting point after 1 h, Ahmad 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 ÷ 6
= 10
(b)
John took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
John's distance is the repeated identity.
Make John's distance the same.
John's distance : Ivan's distance
2 : 6 - 2
2 : 4
John's distance : Ahmad's distance
4 : 6 - 4
4 : 2
John |
Ivan |
Ahmad |
2x2 |
4x2 |
|
4x1 |
|
2x1 |
4 |
8 |
2 |
The distance of John is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
John's rounds : Ivan's rounds : Ahmad's rounds
4 : 8 : 2
Distance that Ahmad completed in 1 h = 1.8 km
2 rounds = 1.8 km = 1800 m
1 round = 1800 ÷ 2 = 900 m
Circumference of the circular track = 900 m
Answer(s): (a) 10; (b) 900 m