Earthquakes

The speed of a P wave is 6000 m/s, so the speed of an S wave is 3000 m/s. Now notice that every second, the P wave travels 3000 meters farther than the S wave. This 3000 meters will take 1 extra second for the S wave to traverse. Therefore, if it takes 30 extra seconds for the S wave to reach, then the distance must be $30\text{ s}\times 6000\text{ m/s}=180000\text{ m}=\boxed{180\text{ km}}$ .

Let the distance be x km.

Speed of S waves= 3000 m/s = 3 km/s

Speed of P waves= 2 * (speed of S wave) = 2 * 3 = 6 km/s

Time for S wave to travel req. distance = x / 3

Time for P wave to travel distance = x / 6

Now, x/3 - x/6 = 30 or, (2x-x)/6 = 30 or, x/6=30 or, x=180 km

The $P$ waves travels at $6000m/s \implies 6km/s$

The time distance between $P$ and $S$ waves are $30s$

The wave runs in $1s \implies 6km$

Then, the waves runs in $30s \implies 6 \times 30 \implies 180 km$

Then the earthquake is $180km$ away.

The speed in which P waves travel is given to be:
$v_p= \frac{6 kilometers}{1 second}$ .
The problem says that the speed of S waves is around half the speed of P waves: $v_s= \frac{v_p}{2} = \frac{6}{2} = \frac{3 kilometers}{1 second}$ .

Instead of setting up a system of equations, I decided to find out how far away something would have to be in order for the difference in the arrival of waves to be 1 second .
After some logic and guess and checking, I found that 6 kilometers away from the Earthquake:
It will take 1 second for P-waves to arrive and 2 seconds for S-Waves to arrive -- The difference in time of arrivals is 1 second every 6 kilometers .

This lets us easily arrive to a final answer:
Distance to Earthquake $= 30 seconds \times \frac{6 kilometers}{1 second} = \boxed{180 kilometers.}$

-It takes the S wave 30 seconds to catch up to the P wave

-The P wave travels twice as fast as the S wave

From these pieces of data we can infer that the S wave would have to have traveled 15 seconds to catch the P wave at half the distance from the earthquake.

Continuing this pattern, we find a geometric series: $\sum_{N=0}^{\infty} 30\cdot \frac{1}{2^N}$

This converges to 60s.

Then, simply multiply to find 60s * 3km/s = 180km

d=s*t=6000x30sec=180000m/s=180000/1000=180km

Vp = 2Vs, (Vp= 6 km/s, Vs = 3 km/s),

6t = 3 (t+30),

t= 30s,

x = 6x30 = 180 km

6000*30/1000 = 180 km

6000 times 30 = 18000 m, so 18000 m = 18 km

6000m-----1s xm-----30s x=180000m x=180 km

6000 meters are equal to 6 kilometer, (the easiest approximation) now we multiply 6 with 30 and we get 180 kilo meters

P wave travel at 6000 metres per second, so it travels 30 x 6000 i.e; 1,80,000 metres in 30 seconds. So 180000 is 180 kms

distance=velocity time here velocity=6000m/s=6km/s time=30s distance=6 30=180 km/s