Harry, Paul and Nick started walking at the same time from the same starting point round a circular track. Nick walked in the clockwise direction. Harry and Paul walked in an anti-clockwise direction. Nick took 12 min to complete each round. He met Harry after every 2 minutes. He met Paul after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Nick complete in 1 h?
- When Nick and Harry met again at the starting point after 1 h, Paul had completed 2.4 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Nick completed in 1 h
= 60 ÷ 12
= 5
(b)
Nick took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Nick's distance is the repeated identity.
Make Nick's distance the same.
Nick's distance : Harry's distance
2 : 12 - 2
2 : 10
Nick's distance : Paul's distance
4 : 12 - 4
4 : 8
Nick |
Harry |
Paul |
2x2 |
10x2 |
|
4x1 |
|
8x1 |
4 |
20 |
8 |
The distance of Nick is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
Nick's rounds : Harry's rounds : Paul's rounds
4 : 20 : 8
Distance that Paul completed in 1 h = 2.4 km
8 rounds = 2.4 km = 2400 m
1 round = 2400 ÷ 8 = 300 m
Circumference of the circular track = 300 m
Answer(s): (a) 5; (b) 300 m