George, Charlie and Owen started walking at the same time from the same starting point round a circular track. Owen walked in the clockwise direction. George and Charlie walked in an anti-clockwise direction. Owen took 12 min to complete each round. He met George after every 2 minutes. He met Charlie after every 7 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Owen complete in 1 h?
- When Owen and George met again at the starting point after 1 h, Charlie had completed 2.4 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Owen completed in 1 h
= 60 ÷ 12
= 5
(b)
Owen took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Owen's distance is the repeated identity.
Make Owen's distance the same.
Owen's distance : George's distance
2 : 12 - 2
2 : 10
Owen's distance : Charlie's distance
7 : 12 - 7
7 : 5
Owen |
George |
Charlie |
2x7 |
10x7 |
|
7x2 |
|
5x2 |
14 |
70 |
10 |
The distance of Owen is the repeated identity.
LCM of 2 and 7 = 14
In 1 h
Owen's rounds : George's rounds : Charlie's rounds
14 : 70 : 10
Distance that Charlie completed in 1 h = 2.4 km
10 rounds = 2.4 km = 2400 m
1 round = 2400 ÷ 10 = 240 m
Circumference of the circular track = 240 m
Answer(s): (a) 5; (b) 240 m