How would you work this word problem?

Question

Math department Development committee members Alan, Amy, Jessica, and Julia were preparing for a conference. They had to pack 1,200 bags of conference material, and they expected to finish packing within the number of hours for which they had budgeted, Jessica packs the fastest, L in one hour. Amy can pack 5 less then Jessica, Julia can pack 10 less then Amy and Alan can pack 5 less then Julia. Once they started, Alan had to leave one hour into it, Jessica left once the agreed time was up. Amy and Julia stayed over 2 hours to finish the job. How many hours was budgeted for packing?

Answer 1

1.  problems of this type are all based on work rates per individual.

2. you state that Jessica can do L per hour and Amy can pack 5 less THAN Jessica, so Jessica's rate per hour is L-5

3.  rate per hour for Julia is L-15; rate per hour for Alan is L-20.

4. # of hours worked are as follows: Alan 1, Jessica x, Amy & Julia x+2 each.

5. each person accomplished packing of a number of bags equal to the product of hours times bags/hour, so the total contributed by Alan, Jessica, Amy & Julia (in that order) is

1(L-20) + x(L) + (x+2)(L-5) + (x+2)(L-15) = 1200.

 

What is missing is the HOURS BUDGETED; once you know that, you have a second equation equating total hours to 1 + x + (x+2) + (x+2). But since that's what is being asked, it must be that quantity L ought to be given, and then one can solve for x.