Final answer:
Without the P-wave speed or the distance to the seismic station, it's not possible to provide an accurate answer to how much longer the secondary waves will arrive after the primary waves.
Step-by-step explanation:
If an S-wave travels at 4 km/s to the same seismic station, and assuming we know the speed at which the P-wave travels, we can calculate the time difference between the arrival of the two different types of waves. The question does not provide the P-wave speed; therefore, we cannot calculate the exact time difference. However, if we were to assume the same conditions as a previous example where the P-wave speed was given as 6 km/s, we could use that speed to find how much longer the S-waves would arrive after the P-waves.
For the given S-wave speed of 4 km/s and a P-wave speed of 6 km/s, the time difference can be calculated based on the distance. Nevertheless, the correct calculation requires specific information regarding the P-wave speed and the distance to the seismic station, which are not provided in this question.