physics help?

Question

When an earthquake occurs, two types of sound waves are generated and travel through the earth. The primary, or P, wave has a speed of about 8.0 km/s and the secondary, or S, wave has a speed of about 4.5 km/s. A seismograph, located some distance away, records the arrival of the P wave and then, 110 s later, records the arrival of the S wave. Assuming that the waves travel in a straight line, how far (in terms of m) is the seismograph from the earthquake?

Answer 1

Fairly simple
for d=distance to seismograph from earthquake, t=time Also, I prefer to use 4.5=9/2.
8 = d/t and 9/2 = d/(t+110)
solving for 'd' put t = d/8 into the second equation
9/2 = d/[(d+880)/8] = 8d/(d+880) cross multiply now
9d + 9*880 = 16d which is
7d = 7920 giving d = 1131.4km or 1.13*10^6 m
(kilometers looks much nicer than meters)

Answer 2

let t be the time the primary waves is recorded, then t + 110 is the the time when secondary wave is recorded

Since both waves are recorded at the same position, their distances are equal

P = S

P = 8t
S = 4.5 (t + 110)

8t = 4.5 (t + 110)
8t = 4.5t + 495
3.5t = 495
t = 141.42s

P = 8 * 141.42
P = 1131.36 km

Answer 3

d/4.5 - d/8 = 110
d = 110*8*4.5/(8 - 4.5)
d ≈ 1,131 km