Final answer:
The center of the earthquake is approximately 646.1 km away.
Step-by-step explanation:
Seismic waves generated by earthquakes consist of both transverse waves (S-waves) and longitudinal waves (P-waves), which propagate at different speeds. The average speed of transverse waves in rock is 9.1 km/s, while the average speed of longitudinal waves is 5.7 km/s. In order to determine the distance to the center of the earthquake, we can use the time difference between the arrival of the transverse and longitudinal waves.
Given that the seismograph records the arrival of the transverse waves 71 s before the arrival of the longitudinal waves, we can use this time difference to calculate the distance. Since we know the speeds of the waves, we can use the formula:
Distance = Speed x Time
Let's denote the distance to the center of the earthquake as d. Using the speed of the transverse waves, we have:
d = (9.1 km/s) x (71 s)
d = 646.1 km
Therefore, the center of the earthquake is approximately 646.1 km away.