Question 692040
Let {{{ t }}} = time in hours for experienced painter
to paint house
{{{ t + 20 }}} = other painter's time in hours to paint house
Add their rates of painting to get rate working together
{{{ 1/t + 1/( t + 20 ) = 1/ 24 }}}
Multiply both sides by {{{ 24t*( t + 20 ) }}}
{{{ 24*( t+20 ) + 24t = t*( t+20 ) }}}
{{{ 24t + 480 + 24t = t^2 + 20t }}}
{{{ t^2 - 28t - 480 = 0 }}} 
I'll complete the square
{{{ t^2 - 28t = 480  }}}
{{{ t^2 - 28t + (28/2)^2 = 480 + (28/2)^2 }}}
{{{ t^2 - 28t + 196 = 480 + 196 }}}
{{{ ( t - 14 )^2 = 676 }}}
{{{ t - 14 = 26 }}}
{{{ t = 40 }}}
{{{ t + 20 = 60 }}}
It takes them 40 hrs for experienced painter 
and 60 hrs for other painter
check:
{{{ 1/t + 1/( t + 20 ) = 1/ 24 }}}
{{{ 1/40+ 1/60 = 1/ 24 }}} 
Multiply both sides by {{{120}}}
{{{ 3 + 2 = 5 }}}
OK