Asher, Billy and Jeremy started walking at the same time from the same starting point round a circular track. Jeremy walked in the clockwise direction. Asher and Billy walked in an anti-clockwise direction. Jeremy took 6 min to complete each round. He met Asher after every 4 minutes. He met Billy after every 5 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Jeremy complete in 1 h?
- When Jeremy and Asher met again at the starting point after 1 h, Billy had completed 2.8 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Jeremy completed in 1 h
= 60 ÷ 6
= 10
(b)
Jeremy took 6 min to complete 1 round
1 min =
16 of circular track = 1 u
6 min =
66 of circular track = 6 u
Jeremy's distance is the repeated identity.
Make Jeremy's distance the same.
Jeremy's distance : Asher's distance
4 : 6 - 4
4 : 2
Jeremy's distance : Billy's distance
5 : 6 - 5
5 : 1
Jeremy |
Asher |
Billy |
4x5 |
2x5 |
|
5x4 |
|
1x4 |
20 |
10 |
4 |
The distance of Jeremy is the repeated identity.
LCM of 4 and 5 = 20
In 1 h
Jeremy's rounds : Asher's rounds : Billy's rounds
20 : 10 : 4
Distance that Billy completed in 1 h = 2.8 km
4 rounds = 2.8 km = 2800 m
1 round = 2800 ÷ 4 = 700 m
Circumference of the circular track = 700 m
Answer(s): (a) 10; (b) 700 m