How Far Did the Earthquake Occur from the Seismic Station?

[jjlandis]

Homework Statement

Earthquakes produce several types of shock waves. The most well-known are the P-waves and the S-waves. In the earth’s crust, the P-waves travel around 7.0 km/s while the S-waves move at about 3.6 km/s. The time delay between the arrival of these two waves at a seismic recording station tells geologists how far away the earthquake occurred. If the time delay is 19 s, how far away from the seismic station did the earthquake occur?
Answer in book is 140.8 m but I can't make it to that answer. Any help would be great.
Thanks.

Homework Equations

The Attempt at a Solution

Tried to find the x distance by using: X-Xo = ((Vox + Vx)*.5)*t

 

[LowlyPion]

Homework Statement

Earthquakes produce several types of shock waves. The most well-known are the P-waves and the S-waves. In the earth’s crust, the P-waves travel around 7.0 km/s while the S-waves move at about 3.6 km/s. The time delay between the arrival of these two waves at a seismic recording station tells geologists how far away the earthquake occurred. If the time delay is 19 s, how far away from the seismic station did the earthquake occur?
Answer in book is 140.8 m but I can't make it to that answer. Any help would be great.
Thanks.

Homework Equations

The Attempt at a Solution

Tried to find the x distance by using: X-Xo = ((Vox + Vx)*.5)*t

The average velocity isn't going to identify the distance now is it since you don't know the actual time really. They arrive at different times.

But they do arrive from the same distance X.

Vs*ts = xs

Vp*tp = xp

where xs = xp = X

Consider then Δt between the slow one and the fast one. That gives you distance then doesn't it? And they do give you conveniently Δt.