SOLUTION: please help me to answer this question. eight men lake 12 days to cultivate a piece of land. after working for 3 days. six more men were employed. how long did they take to cultiva

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Question 1207487: please help me to answer this question. eight men lake 12 days to cultivate a piece of land. after working for 3 days. six more men were employed. how long did they take to cultivate a land
Found 4 solutions by greenestamps, Theo, ikleyn, josgarithmetic:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Total labor required to do the job: 8*12 = 96 man-days.

Amount of labor performed by 8 men in the first 3 days: 8*3 = 24 man-days.

Amount of labor remaining: 96-24 = 72 man-days.

Number of days required to perform the remaining 72 man-days of labor with 8+6 = 14 men: 72/14.

ANSWER: 72/14 days to complete the job after the additional 6 men were employed

Convert the answer into whatever form you want, or whatever form is required.
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the formula used is r * p * t = q

r = rate of each person
p = number of persons
t = time
q = quantity of work.

a basic assumption critical to solving this problem is that each person working on the job works at the same average rate, regardless of the number of people working on the job.

you are given that, when 8 people are working on the job, the job takes 8 days to complete.

the formula becomes r * 8 * 15 = 1

8 is the number of people working on the job.
t is the time it takes to compolete the job.
q is the quantity completed, which is 1 cultivated piece of land.

solve for r to get r = (1/96) = .0104166667.

after working for 3 days, 6 more people were added to the job.

the amount of work completed in 3 days is .0104166667 * 8 * 3 = .25.

that says that 25% of the job was completed in 3 days.

there is 75% of the job to be completed with the additional 6 people that are employed.

the formula becomss .0104166667 * 14 * t = .75

solve for t to get t = 5.142857143 days.

the total time to complete the job is that plus 3 = 8.142857143 days.



Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
please help me to answer this question. eight men lake 12 days to cultivate a piece of land.
after working for 3 days. six more men were employed. how long did they take to cultivate a land
~~~~~~~~~~~~~~~~~~ 


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+6 = 14 workers will complete the remaining job in  


     =  =  =  = 5  days.    ANSWER

Solved.

Usually, in such problems, the problem composers match numbers in a way to get an integer answer.

Then the students are inspired by the beauty of a solution.
They will love  Math.

Other  " math composers "  do not care about it.
Then the students consider such problems as idiotic,  and they are right.
These students will hate  Math.

Such math composers  (of the second kind)  should simply ruthlessly be kicked out of the profession
(using the method of  " iron broom "),  since their activity  IS  OPPOSITE  to goals of education.

-------------------


The solution by @josgarithmetic, giving the answer 9/7 of a day, is INCORRECT.

Simply ignore his post.



Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Normally, 8 men work for 12 days to do 1 job.
r, work rate for 1 man


Work done described,
8 men for 3 days and then 8+6=14 men for some unknown x more days to finish 1 job;











-------------below contains arithmetic mistake-----------------


------ a little over a day with the extra six men to finish
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