Michael, Sam and Daniel started walking at the same time from the same starting point round a circular track. Daniel walked in the clockwise direction. Michael and Sam walked in an anti-clockwise direction. Daniel took 12 min to complete each round. He met Michael after every 2 minutes. He met Sam after every 7 minutes. The three friends kept to their respective speeds throughout their walk.
- How many rounds did Daniel complete in 1 h?
- When Daniel and Michael met again at the starting point after 1 h, Sam had completed 2.4 km. Find the circumference of the circular track in metres.
(a)
1 h = 60 min
Number of rounds that Daniel completed in 1 h
= 60 ÷ 12
= 5
(b)
Daniel took 12 min to complete 1 round
1 min =
112 of circular track = 1 u
12 min =
1212 of circular track = 12 u
Daniel's distance is the repeated identity.
Make Daniel's distance the same.
Daniel's distance : Michael's distance
2 : 12 - 2
2 : 10
Daniel's distance : Sam's distance
7 : 12 - 7
7 : 5
Daniel |
Michael |
Sam |
2x7 |
10x7 |
|
7x2 |
|
5x2 |
14 |
70 |
10 |
The distance of Daniel is the repeated identity.
LCM of 2 and 7 = 14
In 1 h
Daniel's rounds : Michael's rounds : Sam's rounds
14 : 70 : 10
Distance that Sam completed in 1 h = 2.4 km
10 rounds = 2.4 km = 2400 m
1 round = 2400 ÷ 10 = 240 m
Circumference of the circular track = 240 m
Answer(s): (a) 5; (b) 240 m