Question 739724
Add the 3 pipe's rates of filling
( 1 pool filled ) / ( 8 sec ) + ( 1 pool filled ) / ( 12 sec ) + ( 1 pool filled ) / ( 16 sec ) 
= ( 1 pool filled ) / ( t sec )
{{{ 1/8 + 1/12 + 1/16 = 1/t }}}
Multiply both sides by {{{ 48t }}}
{{{ 6t + 4t + 3t = 48 }}}
{{{ 13t = 48 }}}
{{{ t = 3.6923 }}}
With all 3 pipes used, the pool is
filled in 3.6923 sec
check:
{{{ 1/8 + 1/12 + 1/16 = 1/3.6923 }}}
{{{ .125 + .08333 + .0625 = .270833 }}}
{{{ .27083 = .270833 }}}
close enough