Question 850108
Let {{{ t }}} = time in days for A and B 
to complete the work working together
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A and B rate working together:
( 1 job ) / t 
A's rate working alone:
( 1 job ) / ( t + 4 ) 
B's rate working alone:
( 1 job ) / ( t + 16 ) 
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Add their rates to get their rate 
working together
{{{ 1/( t + 4 ) + 1/( t + 16 ) = 1/t }}}
Multiply both sides by {{{ t*( t+4 )*( t+16 ) }}}
{{{ t*( t+16 ) + t*( t+4 ) = ( t+4 )*( t+16 ) }}}
{{{ t^2 + 16t + t^2 + 4t = t^2 + 4t + 16t + 64 }}}
{{{ t^2 = 64 }}}
{{{ t = 8 }}}
It will take them 8 days to complete the work
if they work together
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check:
{{{ 1/( t + 4 ) + 1/( t + 16 ) = 1/t }}}
{{{ 1/( 8 + 4 ) + 1/( 8 + 16 ) = 1/8 }}}
{{{ 1/12 + 1/24 = 1/8 }}}
{{{ 2/24 + 1/24 = 3/24 }}}
OK