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.