Question 683824
Let {{{ n }}} = number of days after starting when 15 men left
The 25 men work at a rate of ( 1 project ) / ( 20 days ), or {{{ 1/20 }}}
What fraction of the project did they complete in {{{ n }}} days?
{{{ (1/20)*n = n/20 }}} of the project
That means that the fraction of the project left to be done is
{{{ 1 - n/20  }}}
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Now there are {{{ 20 - 15 = 5 }}} men left to finish the project
If 25 men work at a rate of {{{ 1/20 }}}, then 5 men will be
5 times slower, or a rate of {{{ (1/5)*(1/20) = 1/100 }}}
Now I can say
{{{ 1/100 = ( 1 - n/20 ) / 37.5 }}}
{{{ .375 = 1 - n/20 }}}
Multiply both sides by {{{ 20 }}}
{{{ 7.5 = 20 - n }}}
{{{ n = 20 - 7.5 }}}
{{{ n = 12.5 }}}
The 15 men left after 12.5 days
check answer:
The original 25 men finished
{{{ n/20 = 12.5/20 }}}
{{{ .625 }}} as a fraction of the project
There was {{{ 1 - .625 = .375 }}} left to do
The remaining 5 men work at a rate of {{{ 1/100 }}}
{{{ 1/100 = .375 / 37.5 }}}
{{{ 37.5/100 = .375 }}}
OK