THERE ARE 3 LIGHT HOUSES,THE FIRST ONE SHINE FOR 3 SECONDS, THEN IS OFF FOR 3 SECONDS.the 2 one shine for 4 seconds then is off for 4 seconds.the 3 one shine for 5 seconds,then is off for 5 seconds.all thr 3 lights have just come together.when is the first time that all the three lights will come off?.when is the next time that all the three lights will come on at the same moment?
The period between the beginning of a "shine" is 6 seconds for #1, 8 seconds for #2 and 10 seconds for #3. the lowest common multiple of those numbers is 2*3*2*2*5 = 120 seconds. That is when they will come ON together for the next time.
When they come OFF together is more complicated. #1 goes off at t = 3, 9, 15, 21, 27, etc s. #2 goes off at 4, 12, 20, 28, 36.. s. One set of number is odd and the other even. The "off" times can never coincide.
Maybe another teacher will prove me wrong about this
To solve this problem, we need to find the points in time when all three lights are either off or on at the same time.
First, let's analyze the on-off pattern of each light individually:
Light 1: On for 3 seconds, off for 3 seconds.
Light 2: On for 4 seconds, off for 4 seconds.
Light 3: On for 5 seconds, off for 5 seconds.
To determine when all three lights are off at the same time, we need to find a common multiple of the off periods for all three lights. The common multiple of 3, 4, and 5 is 60 seconds. Therefore, all three lights will be off together after 60 seconds.
To determine when all three lights will come on at the same moment, we need to find a common multiple of the on periods for all three lights. The common multiple of 3, 4, and 5 is 60 seconds as well. Therefore, all three lights will come on together after 60 seconds.
So, the first time that all three lights will come off together is after 60 seconds, and the next time that all three lights will come on at the same time is also after 60 seconds.