Question 983856
Add their rates of working to get 
their rate working together
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Let {{{ 1/t }}} = Jane's rate of working
expressed as [ 1 job ] / [ t hrs ]
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Mary's rate is:
{{{ 1/( t+3 ) }}} = { 1 job ] / [ t + 3 hrs ] 
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Their rate working together is:
{{{ 1/2 }}} = [ 1 job ] / [ 2 hrs ]
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{{{ 1/t + 1/( t+3 ) = 1/2 }}}
Multiply both sides by {{{ 2t*( t+3 ) }}}
{{{ 2*( t+3 ) + 2t = t*( t+3 ) }}}
{{{ 2t + 6 + 2t = t^2 + 3t }}}
{{{ t^2 - t - 6 = 0 }}}
By looking at this, I see the solution is:
{{{ ( t - 3 )*( t + 2 ) = 0 }}}
Time can't be negative, so the solution is:
{{{ t = 3 }}} hrs
and
{{{ t + 3 = 6 }}} hrs
It takes Mary 6 hrs to finish the job alone
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check answer:
{{{ 1/t + 1/( t+3 ) = 1/2 }}}
{{{ 1/3 + 1/( 3+3 ) = 1/2 }}}
{{{ 2/6 + 1/6 = 1/2 }}}
{{{ 3/6 = 3/6 }}}
OK