Jeremy, Ken and Ethan started walking at the same time from the same starting point round a circular track. Ethan walked in the clockwise direction. Jeremy and Ken walked in an anti-clockwise direction. Ethan took 6 min to complete each round. He met Jeremy after every 4 minutes. He met Ken after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Ethan complete in 1 h?
- When Ethan and Jeremy met again at the starting point after 1 h, Ken had completed 1.5 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 ÷ 6
= 10
(b)
Ethan took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Ethan's distance is the repeated identity.
Make Ethan's distance the same.
Ethan's distance : Jeremy's distance
4 : 6 - 4
4 : 2
Ethan's distance : Ken's distance
5 : 6 - 5
5 : 1
Ethan |
Jeremy |
Ken |
4x5 |
2x5 |
|
5x4 |
|
1x4 |
20 |
10 |
4 |
The distance of Ethan is the repeated identity.
LCM of 4 and 5 = 20
In 1 h
Ethan's rounds : Jeremy's rounds : Ken's rounds
20 : 10 : 4
Distance that Ken completed in 1 h = 1.5 km
4 rounds = 1.5 km = 1500 m
1 round = 1500 ÷ 4 = 375 m
Circumference of the circular track = 375 m
Answer(s): (a) 10; (b) 375 m