Lesson Simple arithmetic word problems on "rate of work"
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<H2>Simple arithmetic word problems on "rate of work"</H2> <H3>Problem 1</H3>A farmer ploughs his land in 12 days if he uses 5 tractors. How long will it take if he uses only 3 tractors? <B>Solution</B> <pre> The entire job is 12*5 = 60 tractor-days. With using only 3 tractors, it will take {{{60/3}}} = 20 days to complete the job. <U>ANSWER</U> </pre> <H3>Problem 2</H3>25 men start a job which they can finish in 40 days. After 16 days 10 men leave. How many days in total did it take for the entire job to be finished? <B>Solution</B> <pre> 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 {{{600/(25-10)}}} = {{{600/15}}} = 40 days. <U>ANSWER</U> </pre> <H3>Problem 3</H3>A certain job can be done by 72 men in 100 days. There were 80 men at the start of the project but after 40 days, 30 of them had to be transferred to another project. How long will it take the remaining workforce to complete the job? <B>Solution</B> <pre> 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. <U>ANSWER</U> </pre> <H3>Problem 4</H3>Eight man take 12 days to cultivate a piece of land. After working for 3 days, 10 more man were employed. How long will it take to 18 man to cultivate the rest of the land ? <B>Solution</B> I will present two solutions. <pre> <U>Solution 1</U> 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. <U>ANSWER</U>. 18 man will complete the remaining part of the job in 4 days. <U>Solution 2</U> 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 {{{9*(8/18)}}} = {{{8/2}}} = 4 days. You get the same answer. </pre> <H3>Problem 5</H3>If 18 pumps can raise 2170 tons of water in 10 days, working 7 hours a day, in how many days will 16 pumps raise 1736 tons of water, working 9 hours a day? <B>Solution</B> <pre> Raising 2170 tons of water requires 18*10*7 = 1260 pump-hours. So, the rate is {{{2170/1260}}} = {{{31/18}}} tons of water per one pump-hour. To raise 1736 tons of water, using 16 pumps working 9 hours a day, {{{1736/((31/18)*16*9)}}} = {{{(1736*18)/(31*16*9)}}} = 7 days is needed. </pre> <H3>Problem 6</H3>Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job 6 days earlier. If the job needs to be completed 32 days earlier, how many additional workers should be hired? <B>Solution</B> Solve it step by step. <pre> 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. <U>ANSWER</U>. 40 additional workers should be hired to complete the job in 32 days earlier. </pre> My other lessons on arithmetic word problems in this site are <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-word-problems-to-solve-them-MENTALLY.lesson>Arithmetic word problems to solve them MENTALLY</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Solving-arithmetic-word-problems-by-reasoning.lesson>Solving arithmetic word problems by reasoning</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-arithmetic-word-problems-solved-in-a-right-way.lesson>Simple arithmetic word problems solved in a right way</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-coin-problems.lesson>Arithmetic coin problems</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-and-simplest-arithmetic-Travel-and-Distanse-problems.lesson>Simple and simplest arithmetic Travel & Distance problems</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Typical-arithmetic-Travel-and-Distance-problems.lesson>Typical arithmetic Travel & Distance problems</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Entertaining-catching-up-arithmetic-Travel-and-Distance-problems.lesson>Entertaining catching up arithmetic Travel & Distance problems</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Other-basic-arithmetic-Travel-and-Distance-problems.lesson>Other basic arithmetic Travel & Distance problems</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-word-problems-on-Travel-and-Distance.lesson>Advanced arithmetic word problems on Travel & Distance</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Finding-travel-time-and-average-rate.lesson>Finding travel time and average rate</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Flying-back-and-forth.lesson>Flying back and forth</A> <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/OVERVIEW-of-lessons-on-arithmetic-word-problems.lesson>OVERVIEW of the first group of lessons on arithmetic word problems</A> To see the whole list of lessons on arithmetic problems, use this link <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-problems-YOUR-ONLINE-TEXTBOOK.lesson>Arithmetic problems - YOUR ONLINE TEXTBOOK</A> It is your way to the entry page of the online textbook on Arithmetic problems.
