Question 854340
Ralph's rate of painting is:
( 1 fence ) / ( 14 hrs )
He paints the fence alone for {{{ 25/60 = 5/12 }}} hr
I can say:
( fraction of the fence he paints ) = ( his rate of painting ) x ( time spent painting )
fraction of the fence he paints = {{{ ( 1/14 )*( 5/12 ) = 5/168 }}}
That means there is {{{ 1 - 5/168 = 163/168 }}}  
of the fence left to paint
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Let {{{ t }}} = the time in hours for them to paint {{{ 163/168 }}}
of the fence painting together
Add their rates of painting to find rate painting together
{{{ 1/14 + 1/16 = ( 163/168 ) / t }}}
Multiply both sides by {{{ 168*2*t = 336t }}}
{{{ 24t + 21t = 326 }}}
{{{ 45t = 326 }}}
{{{ t = 7.2444 }}} hrs
and
{{{ .2444*60 = 14.667 }}} min
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Working together, they finish the fence in 7 hrs 14 min 40 sec
As a simplified fraction, expressed in hours, this is:
{{{ 326/45 }}} hrs
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check answer using calculator:
{{{ 1/14 + 1/16 = ( 163/168 ) / t }}}
{{{ 1/14 + 1/16 = ( 163/168 ) / ( 326/45 ) }}}
{{{ .071429 + .0625 = .97024 / 7.2444 }}}
{{{ .133929 = .133929 }}}
OK