Question 774601
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 
{{{ 14/32 = 7/16 }}} of the job
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There is {{{ 1 - 7/16 = 9/16 }}} of the  job
left to do
The children join them. Add their rates of 
working to find time {{{ t }}} in days to do
{{{ 9/16 }}} of the job
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48 children can do it in 16 days
12 children will take 4 times as long, or 64 days
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12 men take 32 days to complete job
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children's rate: 
( 1 job ) / ( 64 days )
men's rate:
( 1 job ) / ( 32 days )
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{{{ 1/64 + 1/32 = ( 9/16) / t }}}
Multiply both sids by {{{ 64 }}}
{{{ 1 + 2= ( 4*9) / t }}}
{{{ 3 = 36/t }}}
{{{ t = 12 }}}
Working together,  will complete the remaining work in 12 more days
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check:
The 12 men worked a total of {{{ 14 + 12 = 26 }}} days
They finish {{{ 26/32 = 13/16 }}} of the job in this time
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The 12 children worked for 12 days
they finish {{{ 12/64 = 3/16 }}} of the job
{{{ 13/16 + 3/16 = 1 }}} which is 1 job