Michael, Vaidev and Albert started walking at the same time from the same starting point round a circular track. Albert walked in the clockwise direction. Michael and Vaidev walked in an anti-clockwise direction. Albert took 12 min to complete each round. He met Michael after every 2 minutes. He met Vaidev after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Albert complete in 1 h?
- When Albert and Michael met again at the starting point after 1 h, Vaidev had completed 2.1 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Albert completed in 1 h
= 60 ÷ 12
= 5
(b)
Albert took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Albert's distance is the repeated identity.
Make Albert's distance the same.
Albert's distance : Michael's distance
2 : 12 - 2
2 : 10
Albert's distance : Vaidev's distance
6 : 12 - 6
6 : 6
Albert |
Michael |
Vaidev |
2x3 |
10x3 |
|
6x1 |
|
6x1 |
6 |
30 |
6 |
The distance of Albert is the repeated identity.
LCM of 2 and 6 = 6
In 1 h
Albert's rounds : Michael's rounds : Vaidev's rounds
6 : 30 : 6
Distance that Vaidev completed in 1 h = 2.1 km
6 rounds = 2.1 km = 2100 m
1 round = 2100 ÷ 6 = 350 m
Circumference of the circular track = 350 m
Answer(s): (a) 5; (b) 350 m