Question 889057
Let {{{ d }}} = number of days George takes working alone
( 1 house ) / ( d days ) = George's rate
( 1 house ) / ( d-3 days ) = Jerry's rate
( 1 house ) / ( 6 days ) = rate working together
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Add their rates of working to get rate working together
{{{ 1/d + 1/( d-3 ) = 1/6 }}}
Multiply both sides by {{{ 6*d*( d-3 ) }}}
{{{ 6*( d-3 ) + 6d = d*( d-3 ) }}}
{{{ 6d - 18 + 6d = d^2 - 3d }}}
{{{ d^2 - 15d = -18 }}}
Complete the square
{{{ d^2 - 15d + ( 15/2 )^2 = -72/4 + ( 15/2 )^2 }}}
{{{ d^2 - 15d + 225/4 = -72/4 + 225/4 }}}
{{{ ( d - 15/2 )^2 = 153/4 }}}
Take the square root of both sides
{{{ d - 15/2 = sqrt( 153 ) / 2 }}}
{{{ d = ( 15 + sqrt(153) ) / 2 }}}
{{{ d = ( 15 + 12.37 ) / 2 }}}
{{{ d = 27.37/2 }}}
{{{ d = 13.685 }}}
and
{{{ d-3 = 10.685 }}}
George takes 13.7 days working alone
Jerry takes 10.7 days working alone
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check:
{{{ 1/d + 1/( d-3 ) = 1/6 }}}
{{{ 1/13.685 + 1/10.685 = 1/6 }}}
{{{ .07307 + .09359 = .1667 }}}
{{{ .16666 = .1667 }}}
OK
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Note that back when I took the square root of
{{{ 153 }}}, I could have used the negative square root,
but that would have resulted in each one working alone
doing the house faster than working together which
is impossible