Simon, Bobby and Jack started walking at the same time from the same starting point round a circular track. Jack walked in the clockwise direction. Simon and Bobby walked in an anti-clockwise direction. Jack took 6 min to complete each round. He met Simon after every 2 minutes. He met Bobby after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Jack complete in 1 h?
- When Jack and Simon met again at the starting point after 1 h, Bobby had completed 1.6 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Jack completed in 1 h
= 60 ÷ 6
= 10
(b)
Jack took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Jack's distance is the repeated identity.
Make Jack's distance the same.
Jack's distance : Simon's distance
2 : 6 - 2
2 : 4
Jack's distance : Bobby's distance
5 : 6 - 5
5 : 1
Jack |
Simon |
Bobby |
2x5 |
4x5 |
|
5x2 |
|
1x2 |
10 |
20 |
2 |
The distance of Jack is the repeated identity.
LCM of 2 and 5 = 10
In 1 h
Jack's rounds : Simon's rounds : Bobby's rounds
10 : 20 : 2
Distance that Bobby completed in 1 h = 1.6 km
2 rounds = 1.6 km = 1600 m
1 round = 1600 ÷ 2 = 800 m
Circumference of the circular track = 800 m
Answer(s): (a) 10; (b) 800 m