Hello iDrum Originally Posted by

**iDrum** My teacher made this problem up and I'm having a hard time understanding what I'm supposed to do. We haven't worked with earthquake epicenters at all so I'm confused. The last thing we worked with was linear programming. Anyway here's the problem. Thanks for any help!

If you have ever experienced an earthquake, you realize that it causes a primary wave and also a secondary wave to be created. The primary wave (a logitudinal wave) travels faster, so you feel it first. Shortly afterward you will feel the secondary wave (a transverse wave), which we refer to as an aftershock. For our minor earthquake, the primary wave traveled at 6km/s and the secondary wave traveled at 3km/s. In the late afternoon we felt a small earthquake and 4 seconds later came the aftershock. **How far away from the epicenter of the earthquake were we located?**

__Her hint to me was__: *Three equations, three unknowns*.

24 km is the correct answer. It's easy to check: the first wave would take 4 sec to travel that distance, and the second 8 sec, arriving 4 sec later.

But if you don't know that's the answer, here's how you could work it out. Suppose that the first wave had been travelling for $\displaystyle t$ sec before it hit. Then the second was travelling for $\displaystyle (t+4)$ sec. So using the formula

Distance = Speed x Time

we have:

The first wave has travelled a distance $\displaystyle 6t$ km in $\displaystyle t$ sec

The second wave has travelled a distance $\displaystyle 3(t+4)$ km in $\displaystyle (t+4)$ sec

Each wave travels the same distance. Therefore:

$\displaystyle 6t = 3(t+4)$$\displaystyle =3t +12$

$\displaystyle \Rightarrow 3t = 12$

$\displaystyle \Rightarrow t = 4$

So each wave travels $\displaystyle 6t=24$ km.

Grandad