Final answer:
The observer is approximately 20 kilometers away from the earthquake epicenter.
Step-by-step explanation:
In order to determine the distance to the epicenter of an earthquake, you can use the arrival times of the S-wave and P-wave. The S-wave travels at 6 km/s and the P-wave travels at 2 km/s. The time difference between the two waves at a certain point is given as 10 seconds. We can use this information to calculate the distance.
The formula to calculate the distance to the epicenter is:
Distance = Velocity x Time Difference
Plugging in the values, we get:
Distance = 2 km/s x 10 s = 20 km
Therefore, the observer is approximately 20 kilometers away from the earthquake epicenter.