Question 780223
What fraction of the job do A and B get done
working together?
Add their rates of working to get their rate
working together
A's rate: ( 1 job ) / ( 12 days )
B's rate: ( 1 job ) / ( 6 days )
C's rate: ( 1 job ) / ( 3 days )
Let {{{ x }}} = fraction of the job they do in 1 day
I can say:
{{{ 1/12 + 1/6 = x/1 }}}
{{{ x = 1/12 + 2/12 }}}
{{{ x = 3/12 }}}
{{{ x = 1/4 }}}
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They complete {{{ 1/4 }}} of the job, so there is 
{{{ 3/4 }}} left to do
Now with all 3 working, let {{{ t }}} = days
to complete the job
{{{ 1/12 + 1/6 + 1/3 = (3/4)/t }}}
{{{ 1/12 + 2/12 + 4/12 = 9/(12t) }}}
Multiply both sides by {{{ 12 }}}
{{{ 1 + 2 + 4 = 9/t }}}
{{{ 7 = 9/t }}}
{{{ t = 9/7 }}}
1 day has already been spent, so the total days worked is
{{{ 7/7 + 9/7 = 16/7 }}}
(a) 16/7 answer 
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check:
{{{ 1/12 + 1/6 + 1/3 = (3/4)/t }}}
{{{ 1/12 + 2/12 + 4/12 = (3/4) / (9/7) }}}
{{{ 7/12 = (7/9)*(3/4) }}}
{{{ 7/12 = 7/12 }}}
OK