Question 739725
Add Sally and Father's rates of cleaning, then
subtract Dennis's rate of messing up.
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Sally's rate: ( 1 house cleaned ) / ( 8 hrs )
Father's rate: ( 1 house cleaned ) / ( 6 hrs )
Dennis's rate: ( 1 house messed up ) / ( 10 hrs )
Rate with all 3 together: ( 1 house cleaned ) / ( t hrs )
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{{{ 1/8 + 1/6 - 1/10 = 1/t }}}
Multiply both sides by {{{ 240t }}}
{{{ 30t + 40t - 24t = 240 }}}
{{{ 46t = 240 }}}
{{{ t = 5.2174 }}}
{{{ .2174*60 = 13 }}} approximately
It will take 5 hrs and 13 min to clean the house
check:
{{{ 1/8 + 1/6 - 1/10 = 1/5.2174 }}}
{{{ .125 + .16667 - .1 = .19167 }}}
{{{ .19167 = .19167 }}}
OK