SOLUTION: Earthquakes produce several types of shock waves. The most well known are the P-waves (P for primary or pressure) and the S-waves (S for secondary or shear). In the earth's crust,

Question 1204872: Earthquakes produce several types of shock waves. The most well known are the P-waves (P for primary or pressure) and the S-waves (S for secondary or shear). In the earth's crust, P-waves travel at about 6.5 km/s and S-waves move at about 3.5 km/s. The time delay between the arrival of these two waves at a seismic recording station tells geologists how far away an earthquake occurred. If the time delay is 33 seconds, how far from the seismic station did the earthquake occur?
(problem from Young and Freedman. University Physics with Modern Physics. Fifteenth Edition)
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Time taken by S waves - time taken by P waves = 33 s
Let the distance earthquake occured be x km
Time taken by P waves x/6.5 seconds

time taken by s waves = x/3.5 seconds
x/3.5-x/6.5= 33
6.5x-3.5x = 6.5*3.5*33
3x =750.75
x=750.75/3

x= 250.25 Km
The distance the earth quake occured

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Earthquakes produce several types of shock waves. The most well known are the P-waves
(P for primary or pressure) and the S-waves (S for secondary or shear).
In the earth's crust, P-waves travel at about 6.5 km/s and S-waves move at about 3.5 km/s.
The time delay between the arrival of these two waves at a seismic recording station
tells geologists how far away an earthquake occurred. If the time delay is 33 seconds,
how far from the seismic station did the earthquake occur?
(problem from Young and Freedman. University Physics with Modern Physics. Fifteenth Edition)
~~~~~~~~~~~~~~~~~~

Let d be the distance under the question. The travel time for P-wave is seconds (the distance divided by the speed). The travel time for S-wave is seconds (the distance divided by the speed). The difference of these travel times is the time delay - = 33 seconds. It is your basic equation. It is called sometimes "a time equation", because both its parts represent the time. As soon as you got it, the setup is completed. To solve this equations, multiply both sides by 3.5*6.5. You will get then 6.5d - 3.5d = 3.5*6.5*33, or 3d = 750.75. Hence, d = = 250.25. We can round it to 250 km. ANSWER. Earthquack occured 250 km from the seismic station.

Solved.

It is one of many applications of "time equation" methodology to real life problems.

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To see other similar (and different) Travel & Distance problems, look into the lesson
    - Earthquacke waves
in this site.

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