Question 166271: Three lighthouses on three nearby islands flash their lights every evening beginning at 8:35pm. On one island, the ligh flashes every 45 seconds. The lighthouse on the second island has a light that flashes every 2 minutes. The third lighthouse flashes a light every 1 1/4 minutes. At what time will all three lights flash together again?
This is a problem of the week just given to my child on a single piece of paper.
Found 3 solutions by checkley77, scott8148, ankor@dixie-net.com:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! FACTORING EACH OPF THE TIMES IN MINUTES WE THEN FIND THE LOWEST COMMON DENOMINATOR.
45=2*2*2*5
120=2*2*2*3*5
75=3*5*5
NOW WE HAVE 2*2*2*3*5*5=600 MINUTES AFTER 8:35 THEY WILL ALL FLASH.
600MIN.=10 HOURS.
THUS THE TIME WILL BE 8:35 PM+10:00=6:35 AM.
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! you are looking for the lowest common multiple
45sec = 3 * 15
2min = 120sec = 8 * 15
1 1/4 min = 75sec = 5 * 15
LCM = 15 * 3 * 8 * 5 = 1800sec = 30min
so, every half hour they flash together
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! Three lighthouses on three nearby islands flash their lights every evening
beginning at 8:35pm. On one island, the ligh flashes every 45 seconds.
The lighthouse on the second island has a light that flashes every 2 minutes.
The third lighthouse flashes a light every 1 1/4 minutes.
At what time will all three lights flash together again?
:
Convert 2 min to seconds and 1.25 min to seconds.
:
So we have:
:
Lt1 = 45; Lt2 = 120; Lt3 = 75
:
Prime factor each:
45: 3,3,5,
120: 2,2,2,3,5
75: 3,5,5
:
Lcm of all three: 2,2,2,3,3,5,5 Multiply this: 1800 secs they will all Flash
:
1800/60 = 30 min: At 9:05Pm this should occur
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