SOLUTION: if the time (T) it takes to plant rice in an acre varies inversely as the number of the farm workers (W). (a) if 18 workers can plant rice in a certain number of acres in 3 days,

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Question 1171182: if the time (T) it takes to plant rice in an acre varies inversely as the number of the farm workers (W).
(a) if 18 workers can plant rice in a certain number of acres in 3 days, how long will it take 12 workers to plant rice in the same number of acre?
(b) what happens to the time if the number of worker decrease?
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

(a)  The entire job is  18*3 = 54 worker-days.


     12 workers will complete it in   = 4  days = 4.5 days.   ANSWER   <<<---===  edited after the notice by @greenestamps

                                                                    Thanks to @greenestamps (!)




(b)  If the number of worker decreases, the time to complete the job increases.    ANSWER

Solved.

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See the lesson
    - Rate of work problems
in this site.

You will find there many similar and more complicated problems on joint work with solutions and explanations.

Learn the subject from there.


Happy learning (!)



Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


******************

Note to tutor @ikleyn....

The new number of workers is 12, not 8....

******************

With inverse variation, if one of the two quantities changes by a factor of x, the other factor changes by a factor of 1/x.

In the given problem, the number of workers changes by a factor of 12/18 = 2/3; that means the number of days changes by a factor of 3/2.

ANSWER: 3(3/2) = 9/2 or 4.5 days
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