Explain how seismologist determine the distance to the epicenter of a earthquake?
The difference in arrival time between the two types of seismic wave can be used to calculate the distance of the earthquake's epicentre from the seismometer, as the further away an earthquake is, the greater the lag time between the detection of the S waves relative to the P waves.
Based on properties of the crust, and many trials, a seismologist can calculate how far away an earthquake is from a station based just on the S-P lag time.