Tom, Michael and Billy started walking at the same time from the same starting point round a circular track. Billy walked in the clockwise direction. Tom and Michael walked in an anti-clockwise direction. Billy took 5 min to complete each round. He met Tom after every 3 minutes. He met Michael after every 4 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Billy complete in 1 h?
- When Billy and Tom met again at the starting point after 1 h, Michael had completed 2.1 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Billy completed in 1 h
= 60 ÷ 5
= 12
(b)
Billy took 5 min to complete 1 round
1 min =
15 of circular track = 1 u
5 min =
55 of circular track = 5 u
Billy's distance is the repeated identity.
Make Billy's distance the same.
Billy's distance : Tom's distance
3 : 5 - 3
3 : 2
Billy's distance : Michael's distance
4 : 5 - 4
4 : 1
Billy |
Tom |
Michael |
3x4 |
2x4 |
|
4x3 |
|
1x3 |
12 |
8 |
3 |
The distance of Billy is the repeated identity.
LCM of 3 and 4 = 12
In 1 h
Billy's rounds : Tom's rounds : Michael's rounds
12 : 8 : 3
Distance that Michael completed in 1 h = 2.1 km
3 rounds = 2.1 km = 2100 m
1 round = 2100 ÷ 3 = 700 m
Circumference of the circular track = 700 m
Answer(s): (a) 12; (b) 700 m