Question 633181
Let {{{ t }}} = the time it takes the more experienced painter
to paint the house
{{{ t + 20 }}} = time for less experienced painter
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Add their rates of painting to get rate working together
{{{ 1/t + 1/( t + 20 ) = 1/24 }}}
Multiply both sides by {{{ 120t*( t + 20 ) }}}
{{{ 120*( t + 20 ) + 120t  = 5t*( t + 20 ) }}}
{{{ 120t + 2400 + 120t = 5t^2 + 100t }}}
{{{ 5t^2 - 140t - 2400 = 0 }}}
{{{ t^2 - 28t - 480 = 0 }}}
{{{ t^2 -  28t = 480 }}}
Complete the square
{{{ t^2 - 28t + (28/2)^2 = 480 + (28/2)^2 }}}
{{{ t^2 - 28t + 196 = 676 }}}
{{{ ( t - 14 )^2  = 26^2 }}}
{{{ t - 14 = 26 }}}
{{{ t = 40 }}}
40 hrs = the time it takes the more experienced painter
to paint the house
60 hrs = time for less experienced painter