Days on Planet Red are 13 hours long. The animals on Planet Red have regular eating and sleeping habits. The silver snake sleeps for 150 hours, eats for 6 hours, then goes back to sleep. The green walking fish sleeps for 364 hours, eats for 26 hours and then goes back to sleep.The spotted ripplebeast eats for 60 hours, sleeps for 5 hours and then eats again. One day a silver snake, a green walking fish and a spotted ripplebeast all went to sleep at the same time. How many days will pass on Planet Red before these three animals will go to sleep again at exactly the same time?

Question

Days on Planet Red are 13 hours long. The animals on Planet Red have regular eating and sleeping habits. The silver snake sleeps for 150 hours, eats for 6 hours, then goes back to sleep. The green walking fish sleeps for 364 hours, eats for 26 hours and then goes back to sleep.The spotted ripplebeast eats for 60 hours, sleeps for 5 hours and then eats again. One day a silver snake, a green walking fish and a spotted ripplebeast all went to sleep at the same time. How many days will pass on Planet Red before these three animals will go to sleep again at exactly the same time?

Answer 1

I really don't know where to start or what stratedgy to use.

Answer 2

ss period = 150+6 =156 hours

gwf period = 364+26 = 390 hours
sr period = 60+5 = 65 hours

If they all go to sleep at the same time, then an integer number of periods later for all of them, they will fall asleep again.
So we need the least common multiple of those periods.
factor them
156 = 2*2*3*13
390 = 2*5*3*13
65 = 5*13
so we need
2*2*3*5*13 = 780 hours before they all hit the same point in their periods together again.
780/13 = 60 days on this planet

Answer 3

Thanks so much.I worked on this while i was waiting and ended up doing it backwards from you but got the same answer.

150+6=156
156/13=12

364+26=390
390/13=30

60+5=65
65/13=5

60 is the common multipler, so i got 60 days. Is this still right?

Answer 4

To find out how many days will pass on Planet Red before these three animals go to sleep again at exactly the same time, we need to determine the least common multiple (LCM) of the sleeping cycles of the animals.

The silver snake sleeps for 150 hours, eats for 6 hours, then goes back to sleep.
The green walking fish sleeps for 364 hours, eats for 26 hours, then goes back to sleep.
The spotted ripplebeast eats for 60 hours, sleeps for 5 hours, then eats again.

Let's find the LCM of these three cycles by listing the multiples of each cycle until we find a common multiple:

For the silver snake:
150, 300, 450, 600, 750, 900, 1050, 1200, 1350, 1500...

For the green walking fish:
364, 728, 1092, 1456, 1820, 2184, 2548, 2912, 3276, 3640...

For the spotted ripplebeast:
60, 120, 180, 240, 300, 360, 420, 480, 540, 600...

To find the LCM, identify the smallest number that appears in the list for each animal. In this case, it's 1,260.

Therefore, 1,260 hours will pass before these three animals go to sleep again at exactly the same time. Since the days on Planet Red are 13 hours long, we divide 1,260 by 13:

1,260 / 13 = 96.92

So it will take approximately 97 days on Planet Red before the silver snake, green walking fish, and spotted ripplebeast go to sleep again at exactly the same time.