Respuesta :
Answer:
The next time they will all flash together at 8:03 AM.
Step-by-step explanation:
Given : A light flashes every 3 minutes, a second light every 90 seconds, and a third light every 45 seconds. If the three lights flash together at 8:00 AM Monday morning.
To find : When is the next time they will all flash together?
Solution :
First flashes in 3 minutes.
In seconds, 1 minute = 60 second
3 minute = 180 second
Second in 90 seconds.
Third is 45 second.
To get that light flash together we find the LCM of 45,90 and 180.
2 | 45 90 180
2 | 45 45 90
3 | 45 45 45
3 | 15 15 15
5 | 5 5 5
| 1 1 1
[tex]LCM(45,90,180)=2\times 2\times 3\times 3\times 5[/tex]
[tex]LCM(45,90,180)=180[/tex]
Three lights flash together at 180 second.
Convert into minutes,
1 second = [tex]\frac{1}{60}[/tex] minutes
180 second = [tex]\frac{180}{60}[/tex] minutes
180 second = 3 minutes
The three lights flash together after 3 minutes.
Therefore, the next time they will all flash together at 8:03 AM.
