Vincent, Bobby and Luke started walking at the same time from the same starting point round a circular track. Luke walked in the clockwise direction. Vincent and Bobby walked in an anti-clockwise direction. Luke took 12 min to complete each round. He met Vincent after every 2 minutes. He met Bobby after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Luke complete in 1 h?
- When Luke and Vincent met again at the starting point after 1 h, Bobby had completed 1.5 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Luke completed in 1 h
= 60 ÷ 12
= 5
(b)
Luke took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Luke's distance is the repeated identity.
Make Luke's distance the same.
Luke's distance : Vincent's distance
2 : 12 - 2
2 : 10
Luke's distance : Bobby's distance
6 : 12 - 6
6 : 6
Luke |
Vincent |
Bobby |
2x3 |
10x3 |
|
6x1 |
|
6x1 |
6 |
30 |
6 |
The distance of Luke is the repeated identity.
LCM of 2 and 6 = 6
In 1 h
Luke's rounds : Vincent's rounds : Bobby's rounds
6 : 30 : 6
Distance that Bobby 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