Albert, Liam and Oscar started walking at the same time from the same starting point round a circular track. Oscar walked in the clockwise direction. Albert and Liam walked in an anti-clockwise direction. Oscar took 12 min to complete each round. He met Albert after every 2 minutes. He met Liam after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Oscar complete in 1 h?
- When Oscar and Albert met again at the starting point after 1 h, Liam had completed 1.5 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Oscar completed in 1 h
= 60 ÷ 12
= 5
(b)
Oscar took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Oscar's distance is the repeated identity.
Make Oscar's distance the same.
Oscar's distance : Albert's distance
2 : 12 - 2
2 : 10
Oscar's distance : Liam's distance
6 : 12 - 6
6 : 6
Oscar |
Albert |
Liam |
2x3 |
10x3 |
|
6x1 |
|
6x1 |
6 |
30 |
6 |
The distance of Oscar is the repeated identity.
LCM of 2 and 6 = 6
In 1 h
Oscar's rounds : Albert's rounds : Liam's rounds
6 : 30 : 6
Distance that Liam completed in 1 h = 1.5 km
6 rounds = 1.5 km = 1500 m
1 round = 1500 ÷ 6 = 250 m
Circumference of the circular track = 250 m
Answer(s): (a) 5; (b) 250 m