Ryan, Peter and Japheth started walking at the same time from the same starting point round a circular track. Japheth walked in the clockwise direction. Ryan and Peter walked in an anti-clockwise direction. Japheth took 12 min to complete each round. He met Ryan after every 2 minutes. He met Peter after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Japheth complete in 1 h?
- When Japheth and Ryan met again at the starting point after 1 h, Peter had completed 2.7 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Japheth completed in 1 h
= 60 ÷ 12
= 5
(b)
Japheth took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Japheth's distance is the repeated identity.
Make Japheth's distance the same.
Japheth's distance : Ryan's distance
2 : 12 - 2
2 : 10
Japheth's distance : Peter's distance
6 : 12 - 6
6 : 6
Japheth |
Ryan |
Peter |
2x3 |
10x3 |
|
6x1 |
|
6x1 |
6 |
30 |
6 |
The distance of Japheth is the repeated identity.
LCM of 2 and 6 = 6
In 1 h
Japheth's rounds : Ryan's rounds : Peter's rounds
6 : 30 : 6
Distance that Peter completed in 1 h = 2.7 km
6 rounds = 2.7 km = 2700 m
1 round = 2700 ÷ 6 = 450 m
Circumference of the circular track = 450 m
Answer(s): (a) 5; (b) 450 m