Ian, Nick and Albert started walking at the same time from the same starting point round a circular track. Albert walked in the clockwise direction. Ian and Nick walked in an anti-clockwise direction. Albert took 6 min to complete each round. He met Ian after every 3 minutes. He met Nick after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Albert complete in 1 h?
- When Albert and Ian met again at the starting point after 1 h, Nick 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 ÷ 6
= 10
(b)
Albert took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Albert's distance is the repeated identity.
Make Albert's distance the same.
Albert's distance : Ian's distance
3 : 6 - 3
3 : 3
Albert's distance : Nick's distance
5 : 6 - 5
5 : 1
Albert |
Ian |
Nick |
3x5 |
3x5 |
|
5x3 |
|
1x3 |
15 |
15 |
3 |
The distance of Albert is the repeated identity.
LCM of 3 and 5 = 15
In 1 h
Albert's rounds : Ian's rounds : Nick's rounds
15 : 15 : 3
Distance that Nick completed in 1 h = 2.1 km
3 rounds = 2.1 km = 2100 m
1 round = 2100 ÷ 3 = 700 m
Circumference of the circular track = 700 m
Answer(s): (a) 10; (b) 700 m