Ok I figured out a way to do this, but I'm sure there is a faster way, so any advice is greatly appreciated and wanted

The velocity of a shock wave in water is 1500 m/s, while the velocity of sound in air is 330 m/s. The shock wave from a depth charge just beneath the surface of the water is felt by a ship 5.5 s before the sound is heard by the crew. How far is the ship from the explosion.

Here's what I did:

I determined the displacement of the shock wave from the boat, as if it continued to move 1500 m/s for the 5.5 s it took for the sound to reach the ship. So 5.5 seconds times 1500 m/s, which equals 8250 m.

So now I take 8250 m as both the distance of the shockwave from the ship, but also the distance between the shockwave and the sound.

Now I work out a pattern, with a hypothetical Time sequence:

Sound:

0 seconds = travelled 0 meters

1s=330m

2s=660m

3s=990m, etc.

Shockwave:

0 seconds = travelled 0 meters

1s=1500m

2s=3000m

3s=4500m

Displacement between the two:

0 seconds = 0 meters displaced

1s=1170m

2s=1340m

3s=3510m

This means that every second, the shockwave and sound are displaced by 1170m. Therefore, I construct a formula from this:

Displacement=time(in seconds) x 1170 meters or d=t(1170m)

Now, since at the final time, at 5.5 seconds after the shockwave, when the sound is heard at the ship, I've calculated the displacement of the sound and shockwave to be 8250 m, I use the formula:

8250=t x 1170 meters

Therefore, t=8250m/1170m

Therefore, t= 7.051282051... seconds

Now, since I have the time required for that length of displacement, I can answer the question: what is the distance that the ship is from the blast.

So I can do either:

[(7.051282051...)seconds x 1500m/s]-8250m (since the shockwave is 8250m away from the boat)

or

(7.051282051...)seconds x 330m/s

Both equal: 2326.923077 meters, or 2327m (as stated in the text book)

Any tips? Thanks for your time