SOLUTION: It takes 4 men 14 days to do a certain job. How long should it take 7 men working at the same rate to do the same job?

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Question 494362: It takes 4 men 14 days to do a certain job. How long should it take 7 men working at the same rate to do the same job?
Found 4 solutions by Maths68, MathTherapy, josgarithmetic, ikleyn:
Answer by Maths68(1474) About Me  (Show Source):
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4 men do a job in…………………….14 days
Divide by 4 both sides
4/4 men do a job in…………………….14/4 days
1 man does the same job in ……..7/2 days
Multiply by 7 both sides
7*1 man does the same job in ……..7*(7/2) days
7 men will do the same job in …………..49/2 days
7 men will do the same job in …………..24 ½ days

Answer by MathTherapy(10719) About Me  (Show Source):
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It takes 4 men 14 days to do a certain job. How long should it take 7 men working at the same rate to do the same job?
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The other person's answer, that it takes 7 men, 24 days to complete a job that 4 men take 14 days to do, makes ABSOLUTELY
no sense, especially seeing that both groups are working at the same rate. How can a larger group of men take MORE TIME
to a job than a smaller group, when both groups are working at the same rate? RIDICULOUS and NONSENSICAL!!

It'll take the 7 men %284+%2A+14%29%2F7+=+56%2F7+=+highlight%28matrix%281%2C2%2C+8%2C+days%29%29 to do the same job that it takes 4 men, 14 days to complete.

Answer by josgarithmetic(39736) About Me  (Show Source):
You can put this solution on YOUR website!
r, work rate of each man
x, the unknown time for the 7 men
1, the amount of jobs

system%28%284r%29%2A14=1%2C%287r%29%2Ax=1%29

See, each expression on the left equals to 1, so
4%2A14%2Ar=7%2Ax%2Ar
4%2A14=7%2Ax
x=%284%2A14%29%2F7
highlight%28x=8%29

Answer by ikleyn(53618) About Me  (Show Source):
You can put this solution on YOUR website!
.
It takes 4 men 14 days to do a certain job.
How long should it take 7 men working at the same rate to do the same job?
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                This can be solved  MENTALLY  and  MOMENTARILY.


(1)   The whole job is   4 * 14 = 56 man-days.

(2)   7 men will make it in   56/7 = 8 days.         ANSWER

Solved.


It is how my teachers taught us solving such problems 65 years ago.