SOLUTION: Six men working at the same rate can weed a farm in 16 days. After working for 4 days, 2 more men were hired. How long did they take to weed the farm?

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Question 1156875: Six men working at the same rate can weed a farm in 16 days. After working for 4 days, 2 more men were hired. How long did they take to weed the farm?
Found 3 solutions by mananth, josgarithmetic, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
Six men working at the same rate can weed a farm in 16 days. After working for 4 days, 2 more men were hired. How long did they take to weed the farm?



6 men ----16 days
1 man-----x days
1 man does 1/96 of the job in 1 day
6 men will do 6/96 =1/16 of the job in 1 day
they work for 4 days so they complete 4*1/16 of the job = 1/4 of the job
Balance job = 1-(1/4) = 3/4 of the job
8 men will complete 8*1/96 of the job in 1 day= 1/12 of the job

1/12 of the job in 1 day
3/4 of the job in y days
y = (3/4)/(1/12)
y = Balance job in 9 days
9+4 =13 days
The job will be completed in 13 days instead of 16 days

check calc

Answer by josgarithmetic(39735) About Me  (Show Source):
You can put this solution on YOUR website!
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Six men working at the same rate can weed a farm in 16 days.
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r, the rate for one man
For one job of "weed a farm", and 6 men doing this job, 6r%2A16=1.
Or, r=1%2F96.


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After working for 4 days, 2 more men were hired. How long did they take to weed the farm?
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"They" meaning all 6+2=8 men together to finish the job.
highlight_green%286%281%2F96%29%2A4%2B8%281%2F96%29%2Ax=1%29
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6%2A4%2B8x=96
8x=96-24
highlight%28x=9%29--------------------- nine more days after hiring the two more men

Answer by ikleyn(53618) About Me  (Show Source):
You can put this solution on YOUR website!
.
Six men working at the same rate can weed a farm in 16 days. After working for 4 days, 2 more men were hired.
How long did they take to weed the farm?
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        I will show another way to solve, using different reasoning than that in the post by @mananth.

        Its advantage is that NEITHER fractions NOR equations are used. 


The total job is 6 men * 16 days = 96 man-days.


6 men used 6*4 = 24 man-days;  96 - 24 = 72 man-days work remained.


Now 6 + 2 = 8 men work.  They need 72/8 = 9 days to complete the remaining job.


So, 8 men will complete the rest of the job in 9 days.


In all, the whole job will be complete in 4 + 9 = 13 days.

Solved completely, using mental reasoning instead equations and fractions.