Neave, Gabriel and Jack started walking at the same time from the same starting point round a circular track. Jack walked in the clockwise direction. Neave and Gabriel walked in an anti-clockwise direction. Jack took 6 min to complete each round. He met Neave after every 2 minutes. He met Gabriel after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Jack complete in 1 h?
- When Jack and Neave met again at the starting point after 1 h, Gabriel had completed 2.2 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 : Neave's distance
2 : 6 - 2
2 : 4
Jack's distance : Gabriel's distance
4 : 6 - 4
4 : 2
Jack |
Neave |
Gabriel |
2x2 |
4x2 |
|
4x1 |
|
2x1 |
4 |
8 |
2 |
The distance of Jack is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
Jack's rounds : Neave's rounds : Gabriel's rounds
4 : 8 : 2
Distance that Gabriel completed in 1 h = 2.2 km
2 rounds = 2.2 km = 2200 m
1 round = 2200 ÷ 2 = 1100 m
Circumference of the circular track = 1100 m
Answer(s): (a) 10; (b) 1100 m