#### Explanation:

If we call the vehicle's original price when it was bought '$P$', then its price '$p$' after a time '$t$' will be given by:

$p = \frac{P}{t}$

This is a relationship where price is inversely proportional to age.

We don't know $P$, but we can work it out by rearranging the equation and using the data we have:

$P = p t = 3000 \cdot 2 = 6000$

So the car was originally $6000, and after 2 years is worth$3000.

After 6 years its price will be:

$p = \frac{P}{t} = \frac{6000}{6} = 1000$

The car will be worth \$1000 when it is 6 years old.