Howard, Zane and Lee started walking at the same time from the same starting point round a circular track. Lee walked in the clockwise direction. Howard and Zane walked in an anti-clockwise direction. Lee took 12 min to complete each round. He met Howard after every 3 minutes. He met Zane after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Lee complete in 1 h?
- When Lee and Howard met again at the starting point after 1 h, Zane had completed 1.5 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Lee completed in 1 h
= 60 ÷ 12
= 5
(b)
Lee took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Lee's distance is the repeated identity.
Make Lee's distance the same.
Lee's distance : Howard's distance
3 : 12 - 3
3 : 9
Lee's distance : Zane's distance
6 : 12 - 6
6 : 6
Lee |
Howard |
Zane |
3x2 |
9x2 |
|
6x1 |
|
6x1 |
6 |
18 |
6 |
The distance of Lee is the repeated identity.
LCM of 3 and 6 = 6
In 1 h
Lee's rounds : Howard's rounds : Zane's rounds
6 : 18 : 6
Distance that Zane completed in 1 h = 1.5 km
6 rounds = 1.5 km = 1500 m
1 round = 1500 ÷ 6 = 250 m
Circumference of the circular track = 250 m
Answer(s): (a) 5; (b) 250 m