Question 996949
Add their rates of working to get
their rate working together
Let {{{ t }}} = Mary's time to clean the carpets
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Mary's rate working alone:
[ 1 office ] / [ t hrs ]
Henry's rate:
[ 1 office ] / [ t + 9 hrs ]
Working together:
[ 1 ofice ] / [ 6 hrs ]
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{{{ 1/t + 1/( t+9 ) = 1/6 }}}
Multiply both sides by {{{ 6t*( t+9 ) }}}
{{{ 6*( t+9 ) + 6t = t*( t+9 ) }}}
{{{ 6t + 54 + 6t = t^2 + 9t }}}
{{{ t^2 - 3t - 54 = 0 }}}
{{{ ( t - 9 )*( t + 6 ) = 0 }}} ( by looking at it )
{{{ t = 9 }}} ( can't use negative time )
It takes Mary 9 hrs working alone
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check:
{{{ 1/t + 1/( t+9 ) = 1/6 }}}
{{{ 1/9 + 1/(9+9 ) = 1/6 }}}
{{{ 2/18 + 1/18 = 3/18 }}}
{{{ 3/18 = 3/18 }}}
OK