Oscar, Glen and Xavier started walking at the same time from the same starting point round a circular track. Xavier walked in the clockwise direction. Oscar and Glen walked in an anti-clockwise direction. Xavier took 6 min to complete each round. He met Oscar after every 2 minutes. He met Glen after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Xavier complete in 1 h?
- When Xavier and Oscar met again at the starting point after 1 h, Glen had completed 2.9 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Xavier completed in 1 h
= 60 ÷ 6
= 10
(b)
Xavier took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Xavier's distance is the repeated identity.
Make Xavier's distance the same.
Xavier's distance : Oscar's distance
2 : 6 - 2
2 : 4
Xavier's distance : Glen's distance
5 : 6 - 5
5 : 1
Xavier |
Oscar |
Glen |
2x5 |
4x5 |
|
5x2 |
|
1x2 |
10 |
20 |
2 |
The distance of Xavier is the repeated identity.
LCM of 2 and 5 = 10
In 1 h
Xavier's rounds : Oscar's rounds : Glen's rounds
10 : 20 : 2
Distance that Glen completed in 1 h = 2.9 km
2 rounds = 2.9 km = 2900 m
1 round = 2900 ÷ 2 = 1450 m
Circumference of the circular track = 1450 m
Answer(s): (a) 10; (b) 1450 m