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