The velocity of the transverse waves produced by an earthquake is 7.2 km/s, while that of the longitudinal waves is 4.2 km/s. A seismograph records the arrival of the transverse waves 68 s before that of the longitudinal waves. How far away was the earthquake?

Same distance D for both

distance = speed * time
D = 7.2 t
D = 4.2(t+68)
so
7.2 t = 4.2(t+68) solve for t
then use that t in D=7.2 t
to get D, the distance

D = 685.44 km

Thanks a lot!!

To find the distance to the earthquake epicenter, we can use the formula:

Distance = Time * Velocity

Let's start by finding the time it took for the longitudinal waves to arrive. We know that the transverse waves arrived 68 seconds before the longitudinal waves. So, let's denote this as Δt (delta t) and find the total time it took for the longitudinal waves to arrive:

Δt = 68 s

Now, let's find the distance traveled by the transverse waves, using the velocity of the transverse waves:

Distance_transverse = Δt * Velocity_transverse
= 68 s * 7.2 km/s

Next, let's find the total distance traveled by the longitudinal waves, using the velocity of the longitudinal waves:

Distance_longitudinal = (Δt + 68 s) * Velocity_longitudinal
= (68 s + 68 s) * 4.2 km/s

Since the earthquake occurred at some distance away, the total distance traveled by the transverse waves is equal to the distance traveled by the longitudinal waves:

Distance_transverse = Distance_longitudinal

Substituting the values we found earlier:

68 s * 7.2 km/s = (68 s + 68 s) * 4.2 km/s

Now, let's solve this equation to find the distance:

68 s * 7.2 km/s = 136 s * 4.2 km/s

489.6 km = 571.2 km

This equation is not true, which means there might be an error in the provided data or calculation. Please review the problem or double-check the data to ensure accuracy.

To find the distance to the earthquake, we can use the concept of wave velocity and the time difference between the arrival of transverse waves and longitudinal waves.

The formula to calculate distance using wave velocity and time is:

Distance = Wave Velocity * Time

Let's calculate the distance step-by-step:

1. First, we calculate the time it took for the longitudinal waves to arrive after the transverse waves. The time difference is given as 68 seconds.

2. Next, we need to convert the time from seconds to kilometers, since the wave velocity is given in km/s. We will use the velocity of the transverse waves as a reference for time conversion, as the problem states that they arrive first. Since the velocity of the transverse waves is 7.2 km/s, we have:

Time (converted to kilometers) = Velocity of Transverse Waves * Time Difference
Time (converted to kilometers) = 7.2 km/s * 68 s

Therefore, the time in kilometers is 489.6 km.

3. Finally, we can calculate the distance to the earthquake using the velocity of the longitudinal waves:

Distance = Velocity of Longitudinal Waves * Time (converted to kilometers)
Distance = 4.2 km/s * 489.6 km

The distance to the earthquake is approximately 2055.12 km.

So, the earthquake was approximately 2055.12 kilometers away.