P and S waves from an earthquake travel at different speeds and this difference helps in locating the epicenter (point of origin) of the earthquake. (a) Assuming P waves travel at 10.3 km/s and S waves travel at 4.2 km/s, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 3.25 minutes apart

x = 1382.9 km

Explanation:

The speed of the wave is constant, so we can use the uniform motion relationships

p wave

          = x / t₁

          t₁ = x /v_p

S wave

          v_s = x / t₂

           t₂ = x / v_s

indicate that the time difference between the two waves is

          t₂ - t₁ = 3.25 min (60 s / 1 min)

          t₂ -t₁ = 195 s

let's substitute

          = 195

         x ( = 195

let's calculate

         x = 195

         x (0.1410) = 195

         x = 195 /0.141

         x = 1382.9 km