A homeowner empties her hot water heater every 36 days and changes the filter in the heat pump every 48 days. She did both on Friday September 17, 2012. When again will she do both on the same day? (give the day of the week, the date, month, and year)
This is like finding the LCM of 36 and 48
36 = 2x2x3x3
48 = 2x2x2x2x3
LCM = 2x2x2x2x3x3 = 144
So it will happen 144 from Sept 17, 2012
BTW, Sept 17, 2012 was a Monday , not a Friday , so I will let you sort out the rest.
http://www.searchforancestors.com/utility/dayofweek.html
To find out when the homeowner will perform both actions on the same day, we need to find the least common multiple (LCM) of 36 and 48. The LCM represents the smallest number that is evenly divisible by both 36 and 48.
To find the LCM, we can use the prime factorization method. Prime factorize both numbers:
36 = 2^2 * 3^2
48 = 2^4 * 3
To find the LCM, we take the highest power of each prime factor that appears in either number:
2^4 * 3^2 = 144
Therefore, the LCM of 36 and 48 is 144. This means that the homeowner will perform both actions on the same day every 144 days.
Since the actions were last performed on Friday, September 17, 2012, we can calculate when they will be performed again by adding 144 days to that date.
September 17, 2012 + 144 days = January 9, 2013
Therefore, the homeowner will perform both actions on the same day again on Wednesday, January 9, 2013.