Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically, the speed of S wave is about 4.0 km `s^(-1)`, and that of P wave is 8.0 `kms^(-1)`. A seismograph records P and S waved from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, how far away does the earthquake occur?

Explanation

To find the distance to the earthquake based on the arrival times of the P and S waves, we can follow these steps:

### Step 1: Define Variables
Let:
- \( v_1 = 4 \, \text{km/s} \) (speed of S wave)
- \( v_2 = 8 \, \text{km/s} \) (speed of P wave)
- \( t_1 \) = time taken by S wave to reach the seismograph
- \( t_2 \) = time taken by P wave to reach the seismograph
...