Epicenter of an Earthquake - PEER

Student !Using math to find the epicenter of an earthquake6-NotationThe variables are:t p = number of seconds a P wave travels after the instant of the earthquake;t s = number of seconds a S wave travels after the instant of the earthquake;d p = distance (in km) P waves have traveled in t p seconds; andd s = distance (in km) S waves have traveled in t s secondsStep 1: Write an equation that shows how far each type of wave traveled after t seconds.Hint: Use the well-known formula, distance = rate x time,to write the two equations that express distance traveled by the waves in terms of lapsed time. Your answershould be written in the formStep 2:d p = m p t p , and d s = m s t s , where m p and m s are the slopes of the lines.A) Solve each of the two equations from Step 1 for times, t s and t p . Since the distance is the same for eachwave, denote this by D (= d p = d s ).B) Take the difference of the results from Part A; be sure your answer is positive. Denote this difference by thevariable U.C) What does your answer to Part B represent?D) Solve the equation from Part B for distance D.The table below shows four seismic stations near New Mexico (represented by 3- and 4-letter codes) withlatitude and longitude coordinates given in columns 2 and 3. Columns 4 and 5 indicate the times that P and Swaves were received at the stations. The last three blank columns are for arrival time of P- and S-wavesdifferences U, distances D from the stations to the epicenter of the earthquake, and scaled down distances forthe map shown below.StationArrival TimeP-wavesArrival TimeS-waves1. TUC 3:31:25 3:31:542. ANMO 3:31:28 3:32:003. GDL2 3:31:45 3:32:294. LTX 3:32:22 3:33:32Time DiffUDist toEpicenterDScaledDistance forMapKéyah Math 2008!Page!19!