SOLUTION: Sixteen men complete a work in 24 days while 48 children can do it in 16 days. Twelve men startedthe work, after 14 days 12 children joined them. In how Many days will all of them

Question 774601: Sixteen men complete a work in 24 days while 48 children can do it in 16 days. Twelve men startedthe work, after 14 days 12 children joined them. In how Many days will all of them together completethe remaining work?
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Sixteen men complete a work in 24 days
4 men will take 4 times as long, or 96 days
12 men will take 1/3 of this time, or 32 days
In 14 days, the 12 men will complete
of the job
--------------------------
There is of the job
left to do
The children join them. Add their rates of
working to find time in days to do
of the job
--------------------
48 children can do it in 16 days
12 children will take 4 times as long, or 64 days
--------------------
12 men take 32 days to complete job
--------------------
children's rate:
( 1 job ) / ( 64 days )
men's rate:
( 1 job ) / ( 32 days )
------------------

Multiply both sids by

Working together, will complete the remaining work in 12 more days
----------------------------
check:
The 12 men worked a total of days
They finish of the job in this time
---------------
The 12 children worked for 12 days
they finish of the job
which is 1 job

Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
We must infer that "all of them", 12 men plus 12 children.

one-man rate is job per day.
one-child rate is job per day.

Fundamentally, rate*time=jobs, and if job is time split into two parts, then . 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.

Finding this equation was the important part.

SOLVE FOR d.
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