Question

The first P-wave of an earthquake took 11 minutes to travel to a seismic station from the epicenter of the earthquake. What is the seismic station's distance to the epicenter of the earthquake and how long did it take for the first S -wave to travel that distance ?

Answer 1

Answer:

$\large \boxed{\text{5280 km; 25.5 min }}$

Explanation:

1. Distance from epicentre

The average speed of P-waves is about 8 km/s.

(a) Convert minutes to seconds

$\text{Time} = \text{11 min} \times \dfrac{\text{60 s}}{\text{1 min}} = \text{660 s}$

(b) Calculate the distance

$\text{Distance} = \text{ speed} \times \text{time} = \dfrac{\text{8 km}}{\text{1 s}} \times \text{660 s} = \textbf{5280 km}\\\\\text{The seismic station's distance to the epicentre is \large \boxed{\textbf{5280 km}} }$

2. Time for S-wave

The average speed for an S-wave is about 3.45 km/s.

$\begin{array}{rcl}\text{Distance} & = & \text{speed} \times \text{time}\\\text{5280 km} & = & \dfrac{\text{3.45 km}}{\text{1 s}} \times \text{time}\\\\5280 \times \text{1 s} & = & 3.45 \times \text{time}\\\text{Time} & = & \dfrac{\text{5280 s}}{3.45}\\\\ & = & \text{1530 s}\\& = & \textbf{25.5 min}\\\end{array}\\\text{It took the first S-wave \large \boxed{\textbf{25.5 min}} to arrive.}$