An earthquake generates three kinds of waves: surface waves (L waves), which are

Question

An earthquake generates three kinds of waves: surface waves (L waves), which are the slowest and weakest; shear (S) waves, which are transverse waves and carry most of the energy; and pressure (P) waves, which are longitudinal waves and travel the fastest. The speed of P waves is approximately 7.0 km/s, and that of S waves is about 4.0 km/s. Animals seem to feel the P waves. If a dog senses the arrival of P waves and starts barking 34.7 s before an earthquake is felt by humans, approximately how far is the dog from the earthquake

Explanation / Answer

You can say the two waves (P and S) have the following relationship because you're multiply the velocity by how long it takes each wave to travel the same distance (from epicenter to dog):
Vp*t=VS*(t+30.7)

Then plugging in the velocity and solving for t:

7t=4(t+30.7)

t=(4*30.7)/3=40.933 seconds

This is the amount of time it took P to get to the dog, so the distance from the epicenter is

D=Vp*t=7*40.933

D=286.533Km

hope that helps

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