Question 947264
What fraction of the job can the {{{ 3 }}} painters
get done in {{{ 2 }}} days?
They can do {{{ 2/17 }}} of the job
That leaves {{{ 15/17 }}} of the job left to do
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It is assumed ( but they don't say it ) that the
extra {{{ 12 }}} painters work at the same rate as
the first {{{ 3 }}}
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There are {{{ 3 + 12 = 15 }}} painters total after
the 1st 2 days
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{{{ 15 = 3*5 }}}
{{{ 5 }}} times as many painters can work at 
{{{ 5 }}} times the rate, so their rate is 
( 1 job ) / ( 17/5 days )  = {{{ 5/17 }}} 
Now I can say:
{{{ 5/17 = (15/17) / t }}} ( t is time in days )
Multiply both sides by {{{ 17t }}}
{{{ 5t  = 15 }}}
{{{ t = 3 }}}
3 days are required to finish the job
hope I got it