SOLUTION: Seismographs can record two types of wave energy (P waves and S waves) that travel through the Earth after an earthquake. Traveling through granite, P waves travel approximately 5

Algebra ->  Proportions -> SOLUTION: Seismographs can record two types of wave energy (P waves and S waves) that travel through the Earth after an earthquake. Traveling through granite, P waves travel approximately 5       Log On


   

Question 1134751: Seismographs can record two types of wave energy (P waves and S waves) that travel through the Earth after an earthquake. Traveling through granite, P waves travel approximately 5 km/sec and S waves travel approximately 3 km/sec. If a geologist working at a seismic station measures a time difference of 40 sec between an earthquake's P waves and S waves, how far from the epicenter of the earthquake is the station?
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
rate * time = distance
:
let t be the time for P waves to travel the distance, then t+40 is the time for S waves
:
5 * t = 3 * (t + 40)
:
5t = 3t +120
:
2t = 120
:
t = 60 seconds
:
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The station is 5 * 60 = 300 km from the epicenter
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:

Answer by ikleyn(52771) About Me  (Show Source):
You can put this solution on YOUR website!
.

            Another way to solve the problem is THIS : 


Let "d" be the distance from the epicenter of the earthquake to the station, in kilometers.


Then the "time" equation is


    d%2F3 - d%2F5 = 40    seconds.


To solve it, multiply both sides by 15.  You will get


    5d - 3d = 40*15


    2d = 600 


    d = 600/2 = 300 kilometers.      ANSWER

Solved.

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The lesson to learn from my post is THIS : 

    Learn on how to write the "time" equation

    and how to solve it.


The benefit of this approach is in that the equation from the very beginning is written for the unknown value (distance)
and does not introduce an intermediate variable "t" (time).

In school, the traditional method is solving such problems using time.

But a professional way and a method is to write the "time" equation for the unknown distance from the very beginning
and to get the distance from this equation without using the intermediate variable "t".

Ideally when you know and can use EITHER of these two methods.


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See the lesson
    - Earthquake waves
int his site with the solution to similar problem.


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By the way, at an interview it is very easy test to distinct a professional solver from an "amateur".

An "amateur" will solve such problem using time.

A professional solver will use the time equation as I explained it above.