SOLUTION: 6men can weed the farm for 16days.After working for 4 days 2 more men were added. For how long did they weed the farm?

Question 1157255: 6men can weed the farm for 16days.After working for 4 days 2 more men were added. For how long did they weed the farm?
Found 5 solutions by Theo, josgarithmetic, MathTherapy, greenestamps, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the basic assumption here is that they all work at the same rate.
the basic formula is rate * number of people who work at the same rate * time = quantity of work.
that would be n * r * t = q
the quantity of work in this problem is the weeding of one farm.
this makes q = 1.
the number of people who are originally working is 6.
the rate at which each of the men is working needs to be found.
it is initially assumed that the men work the full 16 days, so the formula becomes 6 * r * 16 = 1
now you can solve for r to get r = 1 / (6 * 16) = .0104166667.
replace r in the original formula to test if this value is good.
you get 6 * .0104166667 * 16 = 1, confirming the value is good.
now that you have the rate that each man works at (all assumed to be working at the same rate), you can solve the problem.
the 6 men work at that rate for 4 days.
the formula becomes 6 * .0104166667 * 4 = q
solve for q to get q = .25.
the 6 men finish 1/4 of the job in 4 days.
that stands to reason because 4 is 1/4 of 16.
they have 3/4 of the job left to do, at which time the additional 2 men are added.
the formula becomes 8 * .0104166667 * t = 3/4.
solve for t to get t = (3/4) / (8 * .0104166667) = 9 days.
the total job is finished in 4 + 9 = 13 days.
that's your solution.

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
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..., For how long did they weed the farm?
-------------------------------------

They; the two more men?

-

-

-------------number of days that all 8 men worked TOGETHER to finish.
...
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

6men can weed the farm for 16days.After working for 4 days 2 more men were added. For how long did they weed the farm?

After the 6 men worked for 4 days, of work was completed, so of work remained undone
With 2 more men or 8 men completing the remaining work, and with T being the time the 8 worked, we get:
Time for 8 men to do remaining of work, or
Time it took to weed farm:
ACCEPT NO other answer!!
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The 6 men can to the job in 16 days; in the first 4 days, they can do 1/4 of the job. 3/4 of the job remains.

It would take the 6 men 12 more days to finish the job alone; but now 8 men are working.

Increasing the number of workers by a factor of 4/3 means the remaining job will take 3/4 as long. 3/4 of 12 days is 9 days.

ANSWER: The two added men worked for 9 days; the original 6 men worked for 4+9=13 days.

Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.

Calculations by @josgarithmetic contain an error and, therefore, are invalid.

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

            I also want to contribute.

6 men can do the job in 16 days. It means that the rate of work is = per worker per day. In 4 days, 6 men completed of the job; hence, of the job remained. Now 6 + 2 = 8 men are working for the project. They will complete the job in days = = = 3*3 = 9 days. ANSWER. The crew of 8 workers will complete the remaining job in 9 days. Counting from the very first day, the entire job will be completed in 4 + 9 = 13 days.

Solved.

After the trio of the tutors performed and presented their solutions, @josgarithmetic corrected his calcs.

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On simple and comparatively simple joint work problems see the lessons in this site
    - Rate of work problems
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems" of the section "Word problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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