I believe you are missing some data which could have been useful, for example, do you have a seismogram for each of the three stations LTN (Lennox, Tennessee), POW (Powhatan, Arkansas) and GOIL (Rosebud, Illinois).
You would typically calculate the difference in distance between the stations and the centre of the earthquake using the difference in arrival time between the P- and S-waves, either using a given formula, or a nomogram, or a rule of thumb of 8 km/sec. (very approximate, depends on the geology).
From the known distances, we would draw circles around each station on a map using the calculated distances. The location where the three circles intersect or come close together is the centre of the earthquake, within accuracies of the measurments.
An excellent guide to the exercise, and in fact, the seismographs (page 6) at the three locations of the June 19, 1987 can be found at the following link. The arrival times actually correspond to your (limited) given data.
(Broken Link Removed)
Read through the instructions, and if you need more information, post again.
I looked over the information that you sent and here is what I came up with:
For GOIL:The P arrival time was 3:47:14.6, the difference between P&S was 2.6 seconds and the distance was 37.3km.
For POW: The P arrival time was 3:47:3.0, the S arrival time was 3:47:20.0, the difference between P&S was 17.0 seconds and the distance was 36.1km.
Is this correct?
I still am not sure of what the longitude would be.
I know that the latitude is 36.3 degrees.
Could someone help me with the latitude?
The information I sent you refers to the original seismogramme. If your teacher did not give you this information, you are not supposed to have it. However, it can serve as a check.
Also, I do not know what other information your teacher gave you. For example, you would need the latitude and longitudes of the three stations, see:
But I assume that your teacher would have given you these latitudes and longitudes.
If your teacher gave you the seismographs, you just have to read them off to get the answers. If not, you would need to calculate the values mathematically.
Since the p-wave and s-wave velocities could vary with geology, it may not be accurate to calculate the velocities for LTN and assume the same for all the stations. If your teacher gave you geological information in this respect, it should help.
Finally, after calculating the distance between each station and the location of the earthquake, you will need to draw circles centred on the stations, with a radius equal to the distance, and according to the scale of the map supplied by your teacher.
The point where the three circles meet should be the location of the earthquake (if they meet at one point!)
Using a constant p and s-wave velocities, I have obtained distances. Using the GOIL and LTN data, I have an intersection point at 36.26° latitude and 89.74° longitude. However, the distances of POW do not match the seismograph, so I cannot conclude the results are accurate unless the seismograph is included in the supplied information.