Eric, Jack and Julian started walking at the same time from the same starting point round a circular track. Julian walked in the clockwise direction. Eric and Jack walked in an anti-clockwise direction. Julian took 12 min to complete each round. He met Eric after every 2 minutes. He met Jack after every 7 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Julian complete in 1 h?
- When Julian and Eric met again at the starting point after 1 h, Jack had completed 2.2 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Julian completed in 1 h
= 60 ÷ 12
= 5
(b)
Julian took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Julian's distance is the repeated identity.
Make Julian's distance the same.
Julian's distance : Eric's distance
2 : 12 - 2
2 : 10
Julian's distance : Jack's distance
7 : 12 - 7
7 : 5
Julian |
Eric |
Jack |
2x7 |
10x7 |
|
7x2 |
|
5x2 |
14 |
70 |
10 |
The distance of Julian is the repeated identity.
LCM of 2 and 7 = 14
In 1 h
Julian's rounds : Eric's rounds : Jack's rounds
14 : 70 : 10
Distance that Jack completed in 1 h = 2.2 km
10 rounds = 2.2 km = 2200 m
1 round = 2200 ÷ 10 = 220 m
Circumference of the circular track = 220 m
Answer(s): (a) 5; (b) 220 m