Determining the Location of an Epicenter

Algebra Level 3

To determine the location of an epicenter, seismometers track the difference in time between the arrival of P waves and S waves, since P waves are faster than S waves. With the difference in time between the arrival of P and S waves, one can determine the distance from the epicenter to the seismometer. Then, a circle with a radius of the distance determined is drawn around the seismometer. The same process is repeated with two other seismometers with a circle being drawn around each. The point where all three circles intersect is the location of the epicenter.

Suppose P waves travel at a constant speed of 13,000 m/s while S waves travel at a constant speed of 8,000 m/s. If a seismometer detects a difference of 8.2 seconds between the arrival of P and S waves, what is the distance (in meters) between the seismometer and epicenter?

The answer is 170560.

1 solution

Jesse Li
Jun 3, 2019

The formula for speed is $Speed=\frac{Distance}{Time}$

With that formula, we can determine that $Time=\frac{Distance}{Speed}$

The difference of 8.2 seconds between the arrival of P and S waves is the time it takes for the S waves to arrive minus the time it takes for the P waves to arrive.

Using the formula for time, we can determine the time it takes for the S waves to arrive is $\frac{d}{8000}$ , where $d$ represents the distance between the seismometer and epicenter, and the time it takes for the P waves to arrive is $\frac{d}{13000}$ .

So, $8.2=\frac{d}{8000}-\frac{d}{13000}$ .

We can solve for $d$ by first multiplying both sides by 104,000:

$852800=13d-8d$

$852800=5d$

$\boxed{170560}=d$

Determining the Location of an Epicenter

The answer is 170560.

1 solution

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