> Using 3 microphones and some electronics, the source and destination of a 
> flying bullet can be calculated.  Here's how:
> 
> http://mypeoplepc.com/members/jon8338/math/id21.html 
> 

Nope.   Too many variables and two few data points.  You really only have
two degrees of freedom in the data (Delta t_{12} and Delta t_{13} in your
notation, since Delta t_{23} = Delta t_{13} - Delta t_{12}), and there
are four degrees of freedom in the result you want (two for the unit direction
vector of the bullet, and another two for where the path intersects
a plane normal to that vector).  And all this is under the doubtful assumption
that you know the speed of the bullet.
-- 
Robert Israel              israel@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            Vancouver, BC, Canada