Question 885705
Add their rates of painting to get their
rate painting together
Let {{{ t }}} = time in hours for son to paint
the room working alone
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( 1 room ) / ( 9 hrs ) + ( 1 room ) / ( t hrs ) = ( 1 room ) / ( 6 hrs )
{{{ 1/9 + 1/t = 1/6 }}}
Multiply both sides by {{{ 54t }}}
{{{ 6t + 54 = 9t }}}
{{{ 3t = 54 }}}
{{{ t = 18 }}}
It takes the son 18 hours working alone to paint the room
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check:
{{{ 1/9 + 1/t = 1/6 }}}
{{{ 1/9 + 1/18 = 1/6 }}}
{{{ 2/18 + 1/18 = 3/18 }}}
{{{ 3/18 = 3/18 }}}
OK