Question 749866
Sam's rate is ( 1 house ) / ( 7 days ) = {{{ 1/7 }}}
Betty's rate is ( 1 house ) / ( 42 days ) = {{{ 1/42 }}}
Add their rates to get their rate working together
Let {{{ t }}} = their time in days working together
{{{ 1/7 + 1/42 = 1/t }}}
Multiply both sides by {{{ 42t }}}
{{{ 6t + t = 42 }}}
{{{ 7t = 42 }}}
{{{ t = 6 }}}
Together it takes them 6 days to paint the house