Additional pharmacist

Question

 8 pharmacy technicians worked from 8:00 am until 5:00 pm data entering a set of prescriptions. Working at the same rate, how many ADDITIONAL pharmacy technicians would have been needed for the job to have taken 3 hours LESS?

Answer 1

8:00 am - 5:00 am = 9 hrs worked by each pharmacy technician

9 hrs each * 8 technicians = 72 total hrs worked

 

We want to know how many additional technicians it would take to finish that 72 total hours in 6 actual hours worked by each pharmacy technician.

 

72 total hours / 6 hrs each = 12 pharmacy technicians

12 technicians needed - 8 technicians we have already = x ADDITIONAL pharmacy technicians

 

This should get you far enough that you can finish it.

Answer 2

OK, let's say the pharmacy techs spent the 9 hours (8am to 5pm) entering x prescriptions. That means that each tech entered x/8 prescriptions over the course of the 9 hours, and that it took each tech to enter (x/8)/9hrs to enter each prescription. With the same number of prescriptions (x) and y more techs (a total of 8+y techs), and a goal of taking 6 hours (3 hours less than 9 hours), we can set up a proportion.

 

proportion: (x/8)/9 = (x/(8+y))/6

cross multiply: 6x/8 = 9x/(8+y)

cross multiply: 6x(8+y) = 9x(8)

divide both sides by x: 6(8+y) = 9(8)

multiply out: 48+6y = 72

subtract 48 from both sides: 6y = 24

divide by 6: y = 4

 

So, there would need to be 4 additional techs to make the job take 6 hours instead of 9.

Answer 3

8 · 9 = k

p · 6 = k

 

8 · 9 = p · 6

72 = p · 6

p = 12

 

Four more pharmacists should be hired.