SOLUTION: In working for 10 hours a day , 12 men can do a certain piece of work in 6 days.For how many hours a day must 20 men work in order to do the same amount of work in 14 days?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: In working for 10 hours a day , 12 men can do a certain piece of work in 6 days.For how many hours a day must 20 men work in order to do the same amount of work in 14 days?      Log On


   

Question 1184515: In working for 10 hours a day , 12 men can do a certain piece of work in 6 days.For how many hours a day must 20 men work in order to do the same amount of work in 14 days?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
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10 hours per day versus unknown hours per day
6 days versus 14 days
1 job

12r%2A10%2A6=1, first part of description

20r%2AQ%2A14=1, the question part of description
Q, how many hours per day


20rQ%2A14=12r%2A10%2A6
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Q=%2812%2A10%2A6%29%2F%2820%2A14%29
Q=12%2A3%2F14
Q=6%2A3%2F7
Q=18%2F7
Q=2%264%2F7
This was not rechecked.

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


Given: 10 hours a day for 12 men working 6 days

(1) 20 men instead of 12
The number of men increases by a factor of 20/12=5/3
The number of hours per day decreases by a factor of 5/3 -- i.e., gets multiplied by a factor of 3/5

(2) 14 days instead of 6 days
The number of days increases by a factor of 14/6=7/3
The number of hours per day decreases by a factor of 7/3 -- i.e., gets multiplied by a factor of 3/7

Number of hours per day for 20 men working 14 days:
10%283%2F5%29%283%2F7%29+=+90%2F35+=+18%2F7

ANSWER: 18/7 hours, or 2 4/7 hours, per day for each man