SOLUTION: 8 labourers cut a field in 6 days. (a) how many men will cut the field in 3 days? (b) how long will it take 12 men cut the field? (c) how long will it take 10 men to cut the fie

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 8 labourers cut a field in 6 days. (a) how many men will cut the field in 3 days? (b) how long will it take 12 men cut the field? (c) how long will it take 10 men to cut the fie      Log On


   

Question 1142410: 8 labourers cut a field in 6 days.
(a) how many men will cut the field in 3 days?
(b) how long will it take 12 men cut the field?
(c) how long will it take 10 men to cut the field?
(d) how long will it take 20 labourers cut the field?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
"Cut a field" is one entire job.

n, number of laborers
R, rate of one single laborer
x, amount of time
j, amount of jobs (being 1 for the example problem)
-
highlight_green%28nRx=j%29


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8 laborers cut a field in 6 days.
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8%2Ar%2A6=1
highlight_green%28r=1%2F48%29--------the one-laborer work rate in FIELDS per DAYS

You can solve each of a, b, c, and d using this.

Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.

            I edited the post,  replacing  "cut the field"  by  "plow the field"  and  "labourers"  by  "laborers"  everywhere.


8 laborers plow a field in 6 days.
(a) how many men will plow the field in 3 days?
(b) how long will it take 12 men plow the field?
(c) how long will it take 10 men to plow the field?
(d) how long will it take 20 laborers plow the field?
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Solution

            There are two  ( or three :) )  standard ways to solve problems like these and to explain the solution.

First way 

(a)  The entire work requires  8*6 = 48 labor-days.


     To find how many laborers "x" are needed to complete the job in 3 days, write an equation

         48 = 3x,      (1)

     which immediately gives the solution and the answer

         x = 48/3 = 16 days.


Second way 

(a)  The rate of work of each laborer is  1%2F%288%2A6%29 of the entire job per day in the first case.


     In the second case, the rate of work of each laborer is  1%2F%283%2Ax%29  of the job per day


     Assuming that the rate of work is the same in both cases, you get an equation

         1%2F%288%2A6%29 = 1%2F%283%2Ax%29.


     From the equation, you get 

          8*6 = 3x       ( ! same equation as (1) (!) ),   so

           x  = %288%2A6%29%2F3 = 16.


      You get the same answer.


Third way 

      When you solve such problems several times, you will find it OBVIOUS that two times shorter time period requires two times larger team.


Armed with this knowledge,  you can easily solve the rest of problems by any of these three ways  ON  YOUR  OWN.