Question 864356
Add their rates of laying carpet to
get their rate working together:
2nd carpet layer:
( 1 house ) / ( t hrs )
1st carpet layer:
( 1 house ) / ( t + 4 ) 
working together:
( 1 house ) / ( 3 hrs )
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{{{ 1/t + 1/( t+4 ) = 1/3 }}}
Multiply both sides by {{{ t*( t+4 )*3 }}}
{{{ 3*( t + 4 ) + 3t = t*( t+4 ) }}}
{{{ 3t + 12 + 3t = t^2 + 4t }}}
{{{ t^2 - 2t - 12 = 0 }}}
completing the square:
{{{ t^2 - 2t = 12 }}}
{{{ t^2 - 2t + ( -2/2 )^2 = 12 + ( -2/2 )^2 }}}
{{{ t^2 - 2t + 1 = 12 + 1 }}}
{{{ ( t - 1 )^2 = 13 }}}
Take the square root of both sides
{{{ t - 1 = sqrt(13) }}}
{{{ t = sqrt(13) + 1 }}}
and
{{{ t + 4 = sqrt(13) + 1 + 4 }}}
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These are the answers in hours. Here's the plot 
of the equation {{{ t^2 - 2t - 12 = 0 }}}
{{{ graph( 400, 400, -10, 10, -16, 10, x^2 - 2x - 12 ) }}}
Use the positive solution because you can't
have negative time