SOLUTION: When the Johnson triplets were three weeks old, their sleep habits were remarkably consistent. John slept for 3 hours and was awake for 30 minutes. Joan slept for 2 hours and was a

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Question 220907: When the Johnson triplets were three weeks old, their sleep habits were remarkably consistent. John slept for 3 hours and was awake for 30 minutes. Joan slept for 2 hours and was awake for 30 minutes. Jane slept for 2 hours 20 minutes and was awake for 40 minutes. On October 13 at 8:00 P.M., they all went to sleep at the same time. When did this event occur again? Give both the date and time.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Each one has a different sleep-awake cycle:
John's is
hrs
Joan's is
hrs
Jane's is
hrs
Call the lengths of these cycles ,, and
Now I can say

Note that , and

Finally, I can say

60 sleep-awake cycles for John, 84 sleep-awake cycles for Joan
and 70 sleep-awake cycles for Jane all end together 210 hours
from Oct 13, 8 PM
days
and
hours
8 days would make it Oct 21, 8 PM
Adding 18 hours makes it
Oct 22, 2 PM they all go to sleep again at the same time
check answer
For John:

OK