Carl, Paul and Jeremy started walking at the same time from the same starting point round a circular track. Jeremy walked in the clockwise direction. Carl and Paul walked in an anti-clockwise direction. Jeremy took 5 min to complete each round. He met Carl 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 Jeremy complete in 1 h?
- When Jeremy and Carl 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 Jeremy completed in 1 h
= 60 ÷ 5
= 12
(b)
Jeremy took 5 min to complete 1 round
1 min =
15 of circular track = 1 u
5 min =
55 of circular track = 5 u
Jeremy's distance is the repeated identity.
Make Jeremy's distance the same.
Jeremy's distance : Carl's distance
3 : 5 - 3
3 : 2
Jeremy's distance : Paul's distance
4 : 5 - 4
4 : 1
Jeremy |
Carl |
Paul |
3x4 |
2x4 |
|
4x3 |
|
1x3 |
12 |
8 |
3 |
The distance of Jeremy is the repeated identity.
LCM of 3 and 4 = 12
In 1 h
Jeremy's rounds : Carl's rounds : Paul's rounds
12 : 8 : 3
Distance that Paul completed in 1 h = 2.4 km
3 rounds = 2.4 km = 2400 m
1 round = 2400 ÷ 3 = 800 m
Circumference of the circular track = 800 m
Answer(s): (a) 12; (b) 800 m