The time difference between a 2 km/s S-wave and a 6 km/s P-wave recorded at a monitoring station is 10 seconds. How far away is the earthquake's epicenter?

1. Let d be the distance to the epicenter in kilometres. 2. The S-wave arrival time is d / 2 km/s and the P-wave arrival time is d / 6 km/s. 3. The time difference is (d/2 km/s) minus (d/6 km/s), which simplifies to d/3 km/s. 4. Setting this equal to the given 10 s: d/3 km/s = 10 s. 5. Solving: d = 10 s times 3 km/s = 30 km. 6. Option D, 60 km, comes from the trap of using only the P-wave speed times time and ignoring that the S-wave was also travelling. 7. Option A, 20 km, comes from using only the S-wave speed times time. 8. Option C, 40 km, comes from using the difference of the two speeds directly multiplied by time, which is not the correct relative-arrival relationship. _Source: OpenStax Physics (CC BY 4.0), Ch 13 "Waves and Their Properties", section 13.2 Wave Properties: Speed, Amplitude, Frequency, and Period_