Lesson Simple arithmetic word problems on "rate of work"

Simple arithmetic word problems on "rate of work"

Problem 1

The entire job is 12*5 = 60 tractor-days.


With using only 3 tractors, it will take   = 20 days  to complete the job.    ANSWER

Problem 2

The entire job is 25*40 = 1000 man-days.


After 16 days 25 men completed 16*25 = 400 man-days, and  1000-400 = 600 man-days left to complete.


The answer to the problem's question is   =  = 40 days.   ANSWER

Problem 3

Since the job can be done by 72 men in 100 days, it means that the entire job is 72*100 = 7200 man-days.


80 men in 40 days completed a part of the job, which is 3200 man-days; the remaining job is 7200-3200 = 4000 man-days.


The remaining workforce is 80-30 = 50 men.


They will complete the remaining part of the gob in  4000/50 = 80 days.    ANSWER

Problem 4

              Solution 1


The entire job is 8*12 man-days.


In 3 days,  the part of the job of  3*8 = 24  man-days is complete;
the rest of the job, which is  96-24 = 72 man-days, remains.

Now 8+10 = 18 man work on the remaining part of the job.
They will complete the job in 72/18 = 4 days.


ANSWER.  18 man will complete the remaining part of the job in 4 days.



              Solution 2


After 3 days, 1/4 of the job was done; 3/4 of the job remained.


8 workers would complete the remaining job in 9 days (under regular conditions).


But 8+10 = 18 workers will complete the remaining job in  


     =  = 4  days.    


You get the same answer.

Problem 5

Raising 2170 tons of water requires  18*10*7 = 1260 pump-hours.


So, the rate is   =   tons of water per one pump-hour.


To raise 1736 tons of water, using 16 pumps working 9 hours a day,

     =  = 7 days is needed.

Problem 6

      Step 1 - determine the number of days needed for 5 workers
               to complete the job.


Let d be the number of days for 5 workers to complete the job.

Then the entire job is 5d worker-days.


6 workers could complete the job in (d-6) days.

Hence, from this perspective, the entire work is  6*(d-6)  worker-days.


It gives us this equation

    5d = 6(d-6),

from which we get

     5d = 6d - 36  --->  36 = 6d - 5d  --->  36 = d.


Hence, 5 workers need 36 days to complete the job,  and the entire job is 5*36 = 180 worker-days.



      Step 2 - determine the number of workers needed 
               to complete the job in 32 days earlier.


The question wants the job be complete in 36-32 = 4 days.


It requires 180/4 = 45 workers.



      Step 3 - determine the number of additional workers 
               to be hired.


The number of additional workers is  45 - 5 = 40.


ANSWER.  40 additional workers should be hired to complete the job in 32 days earlier.