physics
posted by Anonymous on .
Earthquakes are essentially sound waves travelling through the earth. They are called seismic waves. Because the earth is solid, it can support both longitudinal and transverse sismic waves, which travel at different speeds. The speed of longitudinal waves, called P waves, is 8982.0 m/s. Transverse waves, called S waves, travel at a slower 4355.0 m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 2.10 min after the P wave, how far away was the earthquake? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.

Distance = (wave speed) x (time)
Let T1 be the time it takes the slower S wave to arrive, and T2 be the time is takes the P wave to arrive.
D = 4355 T1
D = 8982 T2
All you know is T1  T2
T1  T2 = D(1/4355  1/8982) = 126 s
Solve for D
Solve for D. Make sure T is in seconds. D will be im meters 
the answer i got was correct, but how did you get the formula:
T1  T2 = D(1/4355  1/8982) = 126 s ? 
never mind...i figured it out
but when given the question, how did you know that you had to subtract the velocities? 
I did not subtract the velocities. I subtracted the reciprocals of the velocities.
All you know initially is the difference between the wave travel times. You do not know the wave travels times themeselves. (But you can solve for them later).
The equation I used relates the difference in arrival times to the two wave velocities and the distance.