Jack, Ian and Fabian started walking at the same time from the same starting point round a circular track. Fabian walked in the clockwise direction. Jack and Ian walked in an anti-clockwise direction. Fabian took 6 min to complete each round. He met Jack after every 2 minutes. He met Ian after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Fabian complete in 1 h?
- When Fabian and Jack met again at the starting point after 1 h, Ian had completed 2.7 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Fabian completed in 1 h
= 60 ÷ 6
= 10
(b)
Fabian took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Fabian's distance is the repeated identity.
Make Fabian's distance the same.
Fabian's distance : Jack's distance
2 : 6 - 2
2 : 4
Fabian's distance : Ian's distance
4 : 6 - 4
4 : 2
Fabian |
Jack |
Ian |
2x2 |
4x2 |
|
4x1 |
|
2x1 |
4 |
8 |
2 |
The distance of Fabian is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
Fabian's rounds : Jack's rounds : Ian's rounds
4 : 8 : 2
Distance that Ian completed in 1 h = 2.7 km
2 rounds = 2.7 km = 2700 m
1 round = 2700 ÷ 2 = 1350 m
Circumference of the circular track = 1350 m
Answer(s): (a) 10; (b) 1350 m