SOLUTION: Matthew manages the packaging department of his company. Yesterday, the department operated for only 4 hours due to a company picnic, and they only completed 112 packages. Today, h

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Matthew manages the packaging department of his company. Yesterday, the department operated for only 4 hours due to a company picnic, and they only completed 112 packages. Today, h      Log On


   

Question 1148782: Matthew manages the packaging department of his company. Yesterday, the department operated for only 4 hours due to a company picnic, and they only completed 112 packages. Today, his department will complete 43 packages per hour. If Matthew wants to complete packages at an average rate of at least 39 packages per hour, then what is the minimum number of hours that the department must operate today to compensate for yesterday's company picnic?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Matthew manages the packaging department of his company.
Yesterday, the department operated for only 4 hours due to a company picnic, and they only completed 112 packages.
Today, his department will complete 43 packages per hour.
If Matthew wants to complete packages at an average rate of at least 39 packages per hour,
then what is the minimum number of hours that the department must operate today
to compensate for yesterday's company picnic?
:
let t = no. of hrs required to accomplish this
:
%28%28112+%2B+43t%29%29%2F%28%28t+%2B+4%29%29+=+39
multiply both sides by (t+4)
112 + 43t = 39(t + 4)
112 + 43t = 39t + 156
43t - 39t = 156 - 112
4t = 44
t = 44/4
t = 11 hrs has to be worked to average 39 pkg per hr
:
:
Check:
total packages: 112 + 11(43) = 585
total hrs: 4 + 11 = 15 hrs
Average per hour: 585/15 = 39