Question 774601
We must infer that "all of them", 12 men plus 12 children.


one-man rate  is {{{1/(16*24)}}} job per day.
one-child rate is {{{1/(48*16)}}} job per day.


Fundamentally, rate*time=jobs, and if job is time split into two parts, then {{{rate1*time1+rate2*time2=SumOfJobParts}}}.  Agents working at the same time contribute to work rate by simple addition.


The job actually accomplished was done like this:
Let d = Number of days that the 12 children helped in the job.
{{{highlight(12(1/(16*24))14+12(1/(48*16))*d=1)}}}
Finding this equation was the important part.


SOLVE FOR d.