Question 979822
Their rate working together:
[ 1 house cleaned ] / [ 2 hrs ]
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Let {{{ t }}} = Jazlyn's time working alone in hrs
{{{ t + 3 }}} = Anika's time working alone in hrs
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Jazlyn's rate:
[ 1 house cleaned ] / [ t hrs ]
Anika's rate:
[ 1 house cleaned ] / [ t +3 hrs ]
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Add their rates of cleaning to 
get their rate cleaning together
{{{ 1/t + 1/( t+3 ) = 1/2 }}}
Multiply both sides by {{{ t*( t+3 )*2 }}}
{{{ 2*( t+3 ) + 2t = t*( t+3 ) }}}
{{{ 2t + 6 + 2t = t^2 + 3t }}}
{{{ t^2 - t - 6 = 0 }}}
{{{ ( t-3 )*( t+2 ) = 0 }}}
{{{ t = 3 }}} ( time must be positive )
and
{{{ t+3 = 6 }}}
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Jazlyn's time working alone is 3 hrs
Anika's time working alone is 6 hrs
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check:
{{{ 1/t + 1/( t+3 ) = 1/2 }}}
{{{ 1/3 + 1/6 = 1/2 }}}
{{{ 2/6 + 1/6 = 3/6 }}}
{{{ 3/6 = 3/6 }}}
OK