Question 166873: A family is moving and has a number of electronic devices in the same packing crate. One of the devices beepes every 8 minutes, another beeps every 10 minutes and a third beeps every 12 minutes. If all the devices beeped together at 3pm, what time will it be when the all beep together again?
Found 2 solutions by stanbon, ptaylor:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A family is moving and has a number of electronic devices in the same packing crate. One of the devices beepes every 8 minutes, another beeps every 10 minutes and a third beeps every 12 minutes. If all the devices beeped together at 3pm, what time will it be when the all beep together again?
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Find the least common multiple of 8, 10, and 12.
8 = 2^3
10 = 2*5
12 = 2^2*3
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The lcm must have all the prime factors to their highest power present
in the prime factor form of the various factors
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lcm = (2^3)*5*3 = 8*15 = 120 minutes = 2 hours
In 120 minutes the 8 minute beeper will cycle 120/8 = 15 times
The 10 minute beeper will cycle 12 times
The 12 minute beeper will cycle 10 times
When 120 minutes have elapsed they will all beep at once.
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If they all beep at 3pm, they will all beep again at 3pm + 2 hrs = 5pm
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Cheers,
Stan H.
Answer by ptaylor(2198)  (Show Source):
You can put this solution on YOUR website! We determine the LCM for the three beep rates and that's when they will beep together. The LCM for 8, 10 & 12 min is 120 min or two hours. They beep together every two hours or at 5:00pm
CK
The 8 min beeper, beeps 15 times in 2 hours
@3:08-16-24-32-40-48-56-4:04-12-20-28-36-44-52-5:00
The 10 min beeper beeps 12 times in 2 hours
@3:10-20-30-40-50-4:00-10-20-30-40-50-5:00
The 12 min beeper beeps 10 times in 2 hours
@3:12-24-36-48-4:00-12-24-36-48-5:00
Hope this helps---ptaylor
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