Earthquakes generate sound waves inside Earth. Unlike a gas, Earth can experience both transverse (S) and longitudinal (P) sound waves. Typically, the speed of S waves is about 4.5 km/s, and that of P waves 8.0 km/s. A seismograph records P and S waves from an earthquake. The first P waves arrive 3.5 min before the first S waves. If the waves travel in a straight line, how far away did the earthquake occur?

Explanation

To solve the problem, we need to determine how far away the earthquake occurred based on the arrival times of P and S waves. Here’s a step-by-step breakdown of the solution:

### Step 1: Define the Variables
Let:
- \( V_P = 8.0 \, \text{km/s} \) (speed of P waves)
- \( V_S = 4.5 \, \text{km/s} \) (speed of S waves)
- \( t_1 \) = time taken by P waves to reach the seismograph
- \( t_2 \) = time taken by S waves to reach the seismograph
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