Zane, Seth and Carl started walking at the same time from the same starting point round a circular track. Carl walked in the clockwise direction. Zane and Seth walked in an anti-clockwise direction. Carl took 12 min to complete each round. He met Zane after every 3 minutes. He met Seth after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Carl complete in 1 h?
- When Carl and Zane met again at the starting point after 1 h, Seth had completed 2.1 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Carl completed in 1 h
= 60 ÷ 12
= 5
(b)
Carl took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Carl's distance is the repeated identity.
Make Carl's distance the same.
Carl's distance : Zane's distance
3 : 12 - 3
3 : 9
Carl's distance : Seth's distance
6 : 12 - 6
6 : 6
Carl |
Zane |
Seth |
3x2 |
9x2 |
|
6x1 |
|
6x1 |
6 |
18 |
6 |
The distance of Carl is the repeated identity.
LCM of 3 and 6 = 6
In 1 h
Carl's rounds : Zane's rounds : Seth's rounds
6 : 18 : 6
Distance that Seth completed in 1 h = 2.1 km
6 rounds = 2.1 km = 2100 m
1 round = 2100 ÷ 6 = 350 m
Circumference of the circular track = 350 m
Answer(s): (a) 5; (b) 350 m