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 17th, 2012. When will she do both on the same day? ( give the day of the week, date, month and year. also the date is made up and not according to a real calendar)

Question

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 17th, 2012.  When will she do both on the same day? ( give the day of the week, date, month and year.  also the date is made up and not according to a real calendar)

So far, I've computed the LCM for each which comes out to 2^4*3^2= 144. So every 144 days she will do both things at the same time.

After that I added up all the days in each month starting at September 17th, So I got 30-17= 13, then added 13+ 31(Oct)+30(Nov)+31(Dec)+31(Jan)=136, then 144-136=8 so it goes into the next month meaning that the two things will occur together on February 8th.

Then to find the day I started with: 
Friday- 0
Saturday-1 
Sunday-2
Monday-3
Tuesday-4
Wednesday-5
Thursday-6 
Friday-7 
 then 144/7= 140 R4 so it will be on a tuesday.

So, the full answer I got was Tuesday February 8th, 2013.  If someone could just read through this and maybe help me with the part where I need to find the day of the week that would be awesome thanks!

Steve · Answer

Looks pretty good to me. 144/7 = 20 R4 but it's the remainder that counts