Lee, Paul and Neave started walking at the same time from the same starting point round a circular track. Neave walked in the clockwise direction. Lee and Paul walked in an anti-clockwise direction. Neave took 6 min to complete each round. He met Lee after every 3 minutes. He met Paul after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Neave complete in 1 h?
- When Neave and Lee met again at the starting point after 1 h, Paul had completed 2.1 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Neave completed in 1 h
= 60 ÷ 6
= 10
(b)
Neave took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Neave's distance is the repeated identity.
Make Neave's distance the same.
Neave's distance : Lee's distance
3 : 6 - 3
3 : 3
Neave's distance : Paul's distance
4 : 6 - 4
4 : 2
Neave |
Lee |
Paul |
3x4 |
3x4 |
|
4x3 |
|
2x3 |
12 |
12 |
6 |
The distance of Neave is the repeated identity.
LCM of 3 and 4 = 12
In 1 h
Neave's rounds : Lee's rounds : Paul's rounds
12 : 12 : 6
Distance that Paul completed in 1 h = 2.1 km
6 rounds = 2.1 km = 2100 m
1 round = 2100 ÷ 3 = 350 m
Circumference of the circular track = 350 m
Answer(s): (a) 10; (b) 350 m