Final answer:
The distance to the earthquake can be determined by comparing the arrival times of the transverse waves and the longitudinal waves. Using the given velocities and time difference, the distance is calculated to be approximately 184.68828 km.
Step-by-step explanation:
The distance to the epicenter of an earthquake can be determined by comparing the arrival times of the transverse waves (S-waves) and the longitudinal waves (P-waves). In this case, the velocity of the transverse waves is given as 4.79 km/s, and the velocity of the longitudinal waves is 8.5262 km/s. The time difference between the arrival of the transverse waves and the arrival of the longitudinal waves is given as 49.4 seconds. To calculate the distance to the earthquake, we can use the formula:
Distance = Velocity x Time
Let's calculate:
Distance for transverse waves = 4.79 km/s x 49.4 s = 236.526 km
Distance for longitudinal waves = 8.5262 km/s x 49.4 s = 421.21428 km
The distance to the earthquake is the difference between the two distances:
Distance = 421.21428 km - 236.526 km = 184.68828 km
Therefore, the earthquake was approximately 184.68828 km away.