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!

Looks pretty good to me.

144/7 = 20 R4 but it's the remainder that counts

Your calculations and reasoning are correct so far. To find the day of the week for February 8th, 2013, you can utilize the concept of the remainder when dividing by 7.

You have already determined that the remainder is 4 when you divide 144 by 7 (140 remainder 4). This means that after 140 weeks (or 980 days), the day of the week will repeat.

Since you started on a Friday (day 7), you need to count 4 days forward to determine the day of the week for February 8th, 2013.

Therefore, the day of the week for February 8th, 2013, will be Tuesday.

In conclusion, the homeowner will do both tasks (emptying the hot water heater and changing the filter in the heat pump) on Tuesday, February 8th, 2013.