Question 760013
Sarah's rate of working is:
( 1 fence built ) / ( 9 hours )
Joe's rate of working is:
( 1 fence built ) / ( 6 hours )
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If you add their rates of working, you get
their rate working together. 
( Sarah's rate ) + ( Joe's rate ) = ( 1 fence built ) / ( t hours )
Notice that I want t hours to be the time to build 1 fence
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The equation is:
{{{ 1/9 + 1/6 = 1/t }}}
Multiply both sides by {{{ 18t }}}
{{{ 2t + 3t = 18 }}}
{{{ 5t = 18 }}}
{{{ t = 3.6 }}} hrs
{{{ .6*60 = 36 }}}
It will take them 3 hrs and 36 min working together
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t/9=fraction of fence built by Sarah in t hours 
t/6=fraction of fence built by Joe in t hours.
You can arrive at this by multiplying both sides by {{{ t }}}
{{{ t/9 + t/6 = 1 }}}
Time is now eliminated and the equation says:
( Sarah's part ) + ( Joe's part ) = 1 fence built
{{{ 3.6/9 + 3.6/6 = 1 }}}
{{{ 36/9 + 36/6 = 10 }}}
{{{ 4 + 6 = 10 }}}
OK