Answer:
The distance between earthquake center and the measuring station is 1350 kilometers.
Explanation:
Let the earthquake center be at a distance of 'S' meters from the recording station.
Now from the basic relation of distance, speed and time we know that
[tex]Distance=Speed\times Time[/tex]
For a Primary wave (P wave) let us assume that it appraoches the measuring station after [tex]t_{1}[/tex] minutes
Thus making use of the above relation we have
[tex]Distance=V_{p}\times Time\\\\\therefore D=9000\times t_{1}.......(i)[/tex]
Now since it is given that the secondary wave (S wave) reaches the measuring spot after 2 minutes or 120 seconds thus the time taken by secondary waves to reach recorder equals [tex]t_{1}+120[/tex] making use of the same relation we get
[tex]Distance=V_{s}\times Time\\\\\therefore D=5000\times (t_{1}+120).......(ii)[/tex]
Solving equation 'i' and 'ii' we get
[tex]D=5000\times (\frac{D}{9000}+120)\\\\\therefore \frac{D}{5000}=\frac{D}{9000}+120\\\\\frac{D}{5000}-\frac{D}{9000}=120\\\\\therefore D=\frac{120}{\frac{1}{5000}-\frac{1}{9000}}=1350000meters=1350kilomerers[/tex]
