Question 1144753
.
16 workers can complete a piece of work in 30 days. After working for 10 days, 4 more workers joined. 
How many {{{highlight(cross(less))}}} <U>fewer</U> days did the work take?
~~~~~~~~~~~~~~~~~~~~~


<pre>
(1)  Since 16 men can do the job in 30 days, their rate of work is  {{{1/(16*30)}}} part of job per 1 man per day.


(2)  After working for 10 hours, 16 men completed  {{{10/30}}} = {{{1/3}}}  of the job;

     hence,  1 - {{{1/3}}} = {{{2/3}}} remained to complete.


(3)  How many days will it take for 16+4 = 20 men to complete the remaining  {{2/3}}}  of the job ?

     Divide the remaining job by  {{{20/(16*30)}}} = {{{1/24}}}.  You will get

          remaining time =  {{{((2/3))/((1/24))}}} = {{{(2*24)/3}}} = 2*8 = 16 days.


<U>ANSWER</U>.  16 days after 4 men joined.  

         Or, which is the same, 4 days fewer, comparing with the original schedule.
</pre>


/\/\/\/\/\/\/\/


When I see such question &nbsp;"How many fewer days did the work take?", &nbsp;I always ask myself &nbsp;"how many fewer . . . comparing with &nbsp;WHAT ?".


In this form, &nbsp;"How many fewer days did the work take?", &nbsp;the question is &nbsp;UNCOMPLETED &nbsp;(!)