5. If dis the distance from the location of the earthquake to the seismograph and vsis the speed of the
S waves then the time for these waves to reach the seismograph is ts=d/vs. Similarly, the time for P
waves to reach the seismograph is tp=d/vp. The time delay is ∆t=(d/vs)−(d/vp)=d(vp
−vs)/vsvp,
so
d=vsvp∆t
(vp
−vs)=(4.5km/s)(8.0km/s)(3.0min)(60s/min)
8.0km/s−4.5km/s= 1900 km .
We note that values for the speeds were substituted as given, in km/s, but that the value for the time
delay was converted from minutes to seconds.