Paul, Glen and Bobby started walking at the same time from the same starting point round a circular track. Bobby walked in the clockwise direction. Paul and Glen walked in an anti-clockwise direction. Bobby took 12 min to complete each round. He met Paul after every 2 minutes. He met Glen after every 6 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Bobby complete in 1 h?
- When Bobby and Paul met again at the starting point after 1 h, Glen had completed 2.4 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Bobby completed in 1 h
= 60 ÷ 12
= 5
(b)
Bobby took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Bobby's distance is the repeated identity.
Make Bobby's distance the same.
Bobby's distance : Paul's distance
2 : 12 - 2
2 : 10
Bobby's distance : Glen's distance
6 : 12 - 6
6 : 6
Bobby |
Paul |
Glen |
2x3 |
10x3 |
|
6x1 |
|
6x1 |
6 |
30 |
6 |
The distance of Bobby is the repeated identity.
LCM of 2 and 6 = 6
In 1 h
Bobby's rounds : Paul's rounds : Glen's rounds
6 : 30 : 6
Distance that Glen completed in 1 h = 2.4 km
6 rounds = 2.4 km = 2400 m
1 round = 2400 ÷ 6 = 400 m
Circumference of the circular track = 400 m
Answer(s): (a) 5; (b) 400 m