Question 1209086
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Answer: <font color=red>40 extra workers</font>


Explanation


Let's say the job is to move 9000 boxes. 
I'm picking this value since it's a multiple of 5 and 6. 
You can change 9000 to anything else you want to get the same answer at the end.


If there are 5 workers, then each worker handles 9000/5 = 1800 boxes.
Each worker has a unit rate of 1800/x boxes per day.
x is the number of days to finish the job with 5 workers.
rate = amountDone/time


When there are 6 workers, each person now gets 9000/6 = 1500 boxes.
The unit rate per person is 1500/(x-6) where the x-6 refers to finishing the job 6 days early compared to the previous scenario.


If we assume each worker has the same unit rate, then we get this equation
1800/x = 1500/(x-6)
Solving it leads to x = 36.
I'll let the student handle the scratch work.


It takes 36 days for 5 workers to do the job.
It takes 30 days for 6 workers to do the same job.
Each worker moves 50 boxes per day because 1800/36 = 50 or 1500/30 = 50.


n = number of additional workers to hire
n+5 = total number of workers when including the original 5 workers
9000/(n+5) = number of boxes each worker handles
The goal is to finish 32 days early. So instead of taking 36 days it should take 36-32 = 4 days


rate*time = amount done 
(50 boxes per day)*(4 days) = 9000/(n+5) boxes
50*4 = 9000/(n+5)
Solving for n leads to <font color=red>n = 40</font> 
I'll let the student handle the scratch work.


More practice with a similar question is found <a href="https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1079215.html">here</a>
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