Simon, Rael and Jenson started walking at the same time from the same starting point round a circular track. Jenson walked in the clockwise direction. Simon and Rael walked in an anti-clockwise direction. Jenson took 6 min to complete each round. He met Simon after every 2 minutes. He met Rael after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Jenson complete in 1 h?
- When Jenson and Simon met again at the starting point after 1 h, Rael had completed 1.4 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Jenson completed in 1 h
= 60 ÷ 6
= 10
(b)
Jenson took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Jenson's distance is the repeated identity.
Make Jenson's distance the same.
Jenson's distance : Simon's distance
2 : 6 - 2
2 : 4
Jenson's distance : Rael's distance
4 : 6 - 4
4 : 2
Jenson |
Simon |
Rael |
2x2 |
4x2 |
|
4x1 |
|
2x1 |
4 |
8 |
2 |
The distance of Jenson is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
Jenson's rounds : Simon's rounds : Rael's rounds
4 : 8 : 2
Distance that Rael completed in 1 h = 1.4 km
2 rounds = 1.4 km = 1400 m
1 round = 1400 ÷ 2 = 700 m
Circumference of the circular track = 700 m
Answer(s): (a) 10; (b) 700 m