SOLUTION: 12 children working 8 hours a day can clean up their school in 5 days, then 8 children working 19 hours a day will clean the school in how many days.

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Question 1037630: 12 children working 8 hours a day can clean up their school in 5 days, then 8 children working 19 hours a day will clean the school in how many days.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39799) (Show Source):
You can put this solution on YOUR website!
Rate, Time, JOB. The basic rule RT=J, based on rate being , in unit.

N children all working at individual rates R will work at a rate NR.

"Clean their school" is 1 whole job. Put the attention of time on HOURS. Figure the days later.

12 children working 8 hours a day can clean up their school in 5 days,
.

then 8 children working 19 hours a day will clean the school in how many days.
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Let t be the number of HOURS.

The system of equations using time t in hours is .
Two expressions which are both equal to 1.

------------60 hours.

Now finish the answer according to the specified 19 hours per day.

, which is THREE days and maybe some either finishing for part of a day, or a bit of "overtime" during the last of the three days.

Answer by ikleyn(53763) (Show Source):
You can put this solution on YOUR website!
.
12 children working 8 hours a day can clean up their school in 5 days, then 8 children working 19 hours a day will clean the school in how many days.
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The equation is 12*5*8 = 8*x*19. Find x from this equation. The equation says that he number of man-hours (children-hours) is the same in both cases. The problem is so simple and the solution is so obvious that the general theory is not required.