Tommy, Glen and Simon started walking at the same time from the same starting point round a circular track. Simon walked in the clockwise direction. Tommy and Glen walked in an anti-clockwise direction. Simon took 6 min to complete each round. He met Tommy after every 4 minutes. He met Glen after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Simon complete in 1 h?
- When Simon and Tommy met again at the starting point after 1 h, Glen had completed 1.4 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Simon completed in 1 h
= 60 ÷ 6
= 10
(b)
Simon took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Simon's distance is the repeated identity.
Make Simon's distance the same.
Simon's distance : Tommy's distance
4 : 6 - 4
4 : 2
Simon's distance : Glen's distance
5 : 6 - 5
5 : 1
Simon |
Tommy |
Glen |
4x5 |
2x5 |
|
5x4 |
|
1x4 |
20 |
10 |
4 |
The distance of Simon is the repeated identity.
LCM of 4 and 5 = 20
In 1 h
Simon's rounds : Tommy's rounds : Glen's rounds
20 : 10 : 4
Distance that Glen completed in 1 h = 1.4 km
4 rounds = 1.4 km = 1400 m
1 round = 1400 ÷ 4 = 350 m
Circumference of the circular track = 350 m
Answer(s): (a) 10; (b) 350 m