Solving for earthquake transit time via Snell's Law

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SUMMARY

The discussion focuses on solving for earthquake transit time using Snell's Law, specifically addressing the equation for x in terms of known variables. The equation derived is x = (l2*L*v2)/(l1*v1+l2*v2), where l represents the lengths of hypotenuses and L denotes horizontal separation distance. The user expresses confusion regarding the application of Snell's Law and the relationships between angles and variables, particularly θ1, x, L, and H1.

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Homework Statement
Calculate the travel time from Point 1 to Point 2. We know the velocity of
the two media (V1 and V2), the vertical distances to the interface (H1 and H2),
and the horizontal separation distance L.
Relevant Equations
u1sin1 = u2sin2, (x/(v2l2)) - ((L-x)/(v1l1)) = 0, t = (l1/v1) + (l2/v2)
I was told to solve the second equation above for x to get l2 and l2, but that only gets me those in terms of other unknowns. I'm assuming I just need to solve t for my knowns, but I keep getting caught up by my unknowns. i.e., solving for x gives x = (l2*L*v2)/(l1*v1+l2*v2). Please note "l" is a lowercase L. The lowercase denotes the length of the respective hypotenuses while the capital L denotes horizontal separation distance.

I know Snell's law is important here, but I'm not really sure how it helps me.
 

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I presume u1 is the same as v1, etc., and sin1 should be sin(θ1), etc.
What is the relationship between θ1, x, L and H1?
 

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