The time delay between the arrival of these two waves at a seismic recording station tells geologists how far away an earthquake occured. If the time delay in 33s, how far from the seismic station did the earthquake occur?

250.25km

Explanation:

Earthquakes produce different types of shock waves. The most commom are the P-waves (primary) and the S-waves (secondary). The P-waves travel at 6.5 km/s and the S-waves travel at 3.5 km/s. The actual speeds vary depending on the type of material they are going through. The time delay between the arrival of these two waves at a seismic recording station tells geologists how far away the earthquake occurred.

Let the distance of the seismic station from the point of the occurrence of earthquake be taken as x and the time taken for both the P-waves and the S-waves Tp and Ts respectively. Time = Distance divided by speed therefore Tp = x/6.5km/h and Ts = x/3.5km/h. If Ts minus Tp is equal to 33s then:

x/6.5 - x/3.5 = 33

(6.5x - 3.5x)/(6.5 * 3.5) = 33

x = 250.25km

The earthquake occurred 250.25km away from the seismic station.