How far from an earthquake epicenter is a city where the difference between the P-wave and S-wave arrival?

time difference: Δt = 5min 00s = 300s

Distance:

d = 7.5 * Δt = 7.5 * 300 = 2250km

Explanation:

Let Vs is velocity of S-wave and let Vp is velocity of p-wave. S-wave is slower and takes Δt more time to travel the same distance. If t is time needed for P-wave to arrive then distance d is:

d = Vp t ......(1)

and also

d = Vs (t + Δt) ......(2)

From (1) t=d/Vp so we can write (2) as

d = Vs (d/Vp + Δt)

to solve this for d, (as function of Vp and Δt), let's introduce constant k which is ratio k=Vs/Vp :

d = kd + Vs kΔt

d(1-k) = Vs kΔt

d = Vs Δt k/(1-k)

If we take Vs= 5km/s and k=Vs/Vp=0.6

d = Δt * 5 * 0.6/(1-0.6) = 7.5 Δt

Wiki article on seismic waves also says something similar to this:

"A quick way to determine the distance from a location to the origin of a seismic wave less than 200 km away is to take the difference in arrival time of the P wave and the S wave in seconds and multiply by 8 kilometers per second."

http://en.wikipedia.org/wiki/Seismic_wave

Search for a Earth Science NY Regents refrence table then use the chart on earthquake waves

The P wave and S waves are generated on the comparable time from the factor of its beginning referred to as concentration. no longer from epicenter. Epicenter is an imaginary factor only above the factor of concentration in the international floor.the fee and characters are distinctive for the two waves. The P wave travels at a velocity of approximately 13 to 17 ok/m according to 2nd and passes with the aid of all mediums.The shaking would be approximately only one 10th of S wave.strikes the debris interior the path of its propagation. The S wave travels at a velocity of ! : a million.7 ratio. this is continuous for any experience.strikes the debris perpendicular to the path of propagation. based upon the area from the factor of concentration the appearance time of two waves will selection.for instantaneous whilst you're 2 hundred ok/m faraway from concentration you will experience the p wave 25 seconds till now the risky S wave arrives.whilst you're 500 ok/m faraway from concentration you will experience the P wave sixty 3 seconds till now S wave arrives. yet I even have studied a number of activities the place we get sufficient time to circulate to a safer place if we get the caution on the time of arrival of P wave. One such incident became studied with the help of me for the time of my stay in Singapore. the utmost shaking became recorded 2 minute 40 seconds after the recording of typical wave. the area of concentration became 500 ok/m at Sumatra . The P wave arrived quickly because of the fact it could holiday with the aid of sea water.the different waves because of the fact it could no longer holiday with the aid of water it have been given pondered a number of cases under sea and arrived overdue to Singapore. subsequently i'm combating with the seismologist to settle for my earthquake alarm which could alert the persons on the time of arrival of P wave. yet no one got here forward to settle for my concept and my tool. yet I even have issued the caution 2 hours till now Tsunami struck our coast to close by T.V.stations with using my earthquake alarm. i became only criticized with the help of our meteorological branch for my existence saving innovations.