Need advice on triangulation

This is really a brain fart I had from thinking about this homework problem:

But if I have three mics set up in a triangle, a sound source at an unknown location (inside or outside of the triangle) and all I know is which mic the sound reached first, and the time it takes to travel to the other two mics, is there a standard way of triangulating the angle and/or distance?

maybe similar to the way they determine the source of an earthquake (except I dont' know the beginning time of the source...) ?
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If you know the locations of the mics, and the time the sound took to arrive, then you know the distances - assumed that the speed of sound is equal in all directions. This gives you three circles around the mics and the source of the sound has to be on an intersection point of all three circles. However, if you only know which arrived first and then the time gaps for the other two, things are a bit more difficult, since you don't have a scale. In this case you will probably assume a parameter ##d## for the first distance and solve the problem numerically in dependence of ##d##.

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