Glen, Daniel and Ethan started walking at the same time from the same starting point round a circular track. Ethan walked in the clockwise direction. Glen and Daniel walked in an anti-clockwise direction. Ethan took 5 min to complete each round. He met Glen after every 3 minutes. He met Daniel after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Ethan complete in 1 h?
- When Ethan and Glen met again at the starting point after 1 h, Daniel had completed 2.7 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Ethan completed in 1 h
= 60 ÷ 5
= 12
(b)
Ethan took 5 min to complete 1 round
1 min =
15 of circular track = 1 u
5 min =
55 of circular track = 5 u
Ethan's distance is the repeated identity.
Make Ethan's distance the same.
Ethan's distance : Glen's distance
3 : 5 - 3
3 : 2
Ethan's distance : Daniel's distance
4 : 5 - 4
4 : 1
Ethan |
Glen |
Daniel |
3x4 |
2x4 |
|
4x3 |
|
1x3 |
12 |
8 |
3 |
The distance of Ethan is the repeated identity.
LCM of 3 and 4 = 12
In 1 h
Ethan's rounds : Glen's rounds : Daniel's rounds
12 : 8 : 3
Distance that Daniel completed in 1 h = 2.7 km
3 rounds = 2.7 km = 2700 m
1 round = 2700 ÷ 3 = 900 m
Circumference of the circular track = 900 m
Answer(s): (a) 12; (b) 900 m