Question 1166469
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From "a few children", to "made double" that number, the work rate becomes twice what the "few children" were.


How much time to do half the work?
Instead of just half of 18 days, the time would be half of half of 18 days, or {{{9/2}}} or {{{4&1/2}}} days.



The exercise using some algebra---------------------
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{{{R=W/T}}}
Work rate is amount of work divided by time.


If rate depends on how many workers, then for N workers
{{{NR=W/T}}}.


Your example problem:
"a few children", n
"double the amount of children", 2n
Time for n children to do 1 job, 18 days
"a piece of work", W=1
Work rate of one child, r
The time asked in the question, x


{{{system(nr*18=1,2nr*x=1/2)}}}
Solve this system for the value of x.