Simon, Rael and Peter started walking at the same time from the same starting point round a circular track. Peter walked in the clockwise direction. Simon and Rael walked in an anti-clockwise direction. Peter took 12 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 Peter complete in 1 h?
- When Peter and Simon met again at the starting point after 1 h, Rael had completed 2.2 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Peter completed in 1 h
= 60 ÷ 12
= 5
(b)
Peter took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Peter's distance is the repeated identity.
Make Peter's distance the same.
Peter's distance : Simon's distance
2 : 12 - 2
2 : 10
Peter's distance : Rael's distance
4 : 12 - 4
4 : 8
Peter |
Simon |
Rael |
2x2 |
10x2 |
|
4x1 |
|
8x1 |
4 |
20 |
8 |
The distance of Peter is the repeated identity.
LCM of 2 and 4 = 4
In 1 h
Peter's rounds : Simon's rounds : Rael's rounds
4 : 20 : 8
Distance that Rael completed in 1 h = 2.2 km
8 rounds = 2.2 km = 2200 m
1 round = 2200 ÷ 8 = 275 m
Circumference of the circular track = 275 m
Answer(s): (a) 5; (b) 275 m