Justin, Owen and Henry started walking at the same time from the same starting point round a circular track. Henry walked in the clockwise direction. Justin and Owen walked in an anti-clockwise direction. Henry took 6 min to complete each round. He met Justin after every 3 minutes. He met Owen after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Henry complete in 1 h?
- When Henry and Justin met again at the starting point after 1 h, Owen had completed 1.8 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Henry completed in 1 h
= 60 ÷ 6
= 10
(b)
Henry took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Henry's distance is the repeated identity.
Make Henry's distance the same.
Henry's distance : Justin's distance
3 : 6 - 3
3 : 3
Henry's distance : Owen's distance
5 : 6 - 5
5 : 1
Henry |
Justin |
Owen |
3x5 |
3x5 |
|
5x3 |
|
1x3 |
15 |
15 |
3 |
The distance of Henry is the repeated identity.
LCM of 3 and 5 = 15
In 1 h
Henry's rounds : Justin's rounds : Owen's rounds
15 : 15 : 3
Distance that Owen completed in 1 h = 1.8 km
3 rounds = 1.8 km = 1800 m
1 round = 1800 ÷ 3 = 600 m
Circumference of the circular track = 600 m
Answer(s): (a) 10; (b) 600 m