Question 982505
Let {{{ x }}} = the fraction of the job they
do working together for 2 hrs
Aira's rate of working is:
[ 1 job done / 4 hrs ]
Queenie's rate of working is:
[ 1 job done / 9 hrs ]
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Add their rates of working to get
their rate working together
Their rate working together is: {{{ x/2 }}}
{{{ 1/4 + 1/9 = x/2 }}}
Multiply both sides by {{{ 36 }}}
{{{ 9 + 4 = 18x }}}
{{{ 18x = 13 }}}
{{{ x = 13/18 }}}
In 2 hrs, they do {{{ 13/18 }}} of the work. That 
means there is {{{ 1 - 13/81 = 5/18 }}} 
of the work left to do
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Let {{{ t }}} = time in hrs for Aira to 
finish the job
{{{ 1/4 = (( 5/18 )) / t }}}
{{{ 1/4 = 5/(18t) }}}
Multiply both sides by {{{ 36t }}}
{{{ 9t = 10 }}}
{{{ t = 10/9 = 1 + 1/9 }}}
{{{ ( 1/9 )*60 = 6 + 2/3 }}}
{{{ ( 2/3)*60 = 40 }}}
---------------------
Aira finishes the job in 1 hr 6 min 40 sec
check answer:
{{{ 1/4 = (( 5/18 )) / t }}}
{{{ 1/4 = (( 5/18 )) / (( 10/9 )) }}}
{{{ 1/4 = ( 5/18 )*( 9/10 ) }}}
{{{ 1/4 = ( 5/10 )*( 9/18 ) }}}
{{{ 1/4 = ( 1/2 )*( 1/2 ) }}}
{{{ 1/4 = 1/4 }}}
OK
Hope I got it!