Question 984443
Let {{{ x }}} = the fraction of the job that
A & B get done in 8 hrs
{{{ 1 - x }}} = the fraction of the job left 
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After B stops working, A works at the rate:
{{{ ( 1 - x ) / 2 }}} and finishes job
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You are told that A's rate is twice B's so
B's rate must be: {{{ ( 1 - x ) / 4 }}}
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Add their rates of working to get their rate 
working together:
{{{ ( 1 - x ) / 2 + ( 1 - x ) / 4 = x / 8 }}}
Multiply both sides by {{{ 8 }}}
{{{ 4*( 1 - x ) + 2*( 1 - x ) = x }}}
{{{ 4 - 4x + 2 - 2x = x }}}
{{{ 7x = 6 }}}
{{{ x = 6/7 }}}
and
{{{ 1 - x = 1 - 6/7 }}}
{{{ 1 - x = 1/7 }}}
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So, A can do 1/7 of the job in 2 hrs
{{{ ( 1/7 ) / 2 = 1/14 }}}
A can do the whole job in 14 hrs
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This is twice B's rate, so B will take
28 hrs to do the job alone
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check:
{{{ ( 1 - x ) / 2 + ( 1 - x ) / 4 = x / 8 }}}
{{{ ( 1/7 ) / 2 + ( 1/7 ) / 4 = ( 6/7 ) / 8 }}}
{{{ 1/14 + 1/28 = 6/56 }}}
{{{ 2/28 + 1/28 = 3/28 }}}
{{{ 3/28 = 3/28 }}}
OK