# Thread: Equitable Pull from Pool of Hours by Month

1. ## Equitable Pull from Pool of Hours by Month

Hi, math whizzes. Have a business problem. This is not homework, but rather a problem I need to figure out at work...

Suppose an employee has been allotted 500 hours to work over the period of 1/18/2017 through 6/13/2017. I need to get the expected number of hours they'll work per month during the 6-month period. If the date range were 1/1/2017 through 6/30/2017, then the problem would be simple to solve by doing an average (83.33... hours per month). But when they don't start on the first day of a month or end on a last day of month, this is where I need help. Conceptually, I am thinking that partial start/end months need to have the same 'pull' from the 500-hour allotment as the full months in between (in this case Feb. - May). So immediately weighted averages, or something of the sort, comes to mind. But I'm not sure how to apply this concept mathematically.

Any ideas on how to how to solve my problem?

Greatly appreciated!!!!!!

2. ## Re: Equitable Pull from Pool of Hours by Month

14+28+31+30+31+13 = 147 days

(500 hrs)/(147 days) is about 3.4 hrs per day, so multiply the number of days in that month by 3.4 ...

April has 30 days times 3.4 is 102 hrs. So, for what I assume is 20 work days in April (weekends off), about 5.1 hrs a day in that month.

Something like that?

3. ## Re: Equitable Pull from Pool of Hours by Month

Thanks so much, skeeter, for taking the time to reply to my post!

I swear I was thinking about taking that exact same approach, just didn't know if there was a more 'mathy' approach using something like weighted averages... Like, January and June have partial pulls from the 500-hour allotment, which I'd expect to increase the Feb. through May pulls -or something like that. In my head, conceptually, I know how this should be approached; I just cannot express it mathematically.

Again, many thanks for the proposal. I might just end up taking this route. :-)

4. ## Re: Equitable Pull from Pool of Hours by Month

Approximately, 1/18 to 1/31 is about half a month and 6/1 to 6/13 is about half a month. There are four full months so that time is approximately 5 months so the average per month is, approximately, 5000/5= \$1000 per month.

If you want a more accurate answer then calculate exactly how many days there are there 1/18/2017 to 6/13/2017. The average per day is 500 divided by the number of days. Then calculate the number of days in each month- there will be 13 days left in January, 28 days in February, 31 in March, 30 in April, 31 in May, and 13 in June. Multiply each of those by the average per day to get the amount for each of the 6 months, then average those values.

5. ## Re: Equitable Pull from Pool of Hours by Month

Much appreciated, HallsofIvy! Now I have two fine approaches to use. Really appreciate the thoughtful feedback!