Final answer:
The distance to the epicenter of an earthquake can be calculated using the travel times and velocities of s-waves and p-waves. By equating the two expressions for distance and solving for the p-wave travel time, we find that the epicenter is approximately 24.3 km away, which does not match any of the provided options.
Step-by-step explanation:
The question asks how far the epicenter of an earthquake is from a certain point if a 2.00 km/s s-wave and a 6.00 km/s p-wave are recorded with a time difference of 5.40 seconds. To calculate the distance to the epicenter (d), we use the formula d = v_p × t_p = v_s × t_s, where v_p and v_s are the velocities of the p-wave and s-wave, respectively, and t_p and t_s are their travel times. Since the s-wave and p-wave were recorded with a time difference of 5.40 seconds, we can express the travel time of the s-wave as t_s = t_p + 5.40. Now we can write two equations:
1. d = 6.00 km/s × t_p
2. d = 2.00 km/s × (t_p + 5.40 s)
By equating the two expressions for d and solving for t_p, we get: 6.00 km/s × t_p = 2.00 km/s × (t_p + 5.40 s). Solving this yields t_p = 4.05 s. Then we can calculate the distance using either equation, and we get d = 6.00 km/s × 4.05 s = 24.3 km. The closest listed answer to 24.3 km is option d. 15 km, which appears to be incorrect based on our calculations.