You receive orders to sail due east for $24.5\mathbf{}\mathbf{mi}$ to put your salvage ship directly over a sunken pirate ship. However, when your divers probe the ocean floor at that location and find no evidence of a ship, you radio back to your source of information, only to discover that the sailing distance was supposed to be $24.5\mathbf{}\mathbf{nautical}\mathbf{}\mathbf{miles}$, not regular miles. Use the Length table in Appendix D to calculate how far horizontally you are from the pirate ship in kilometers.

The sailing distance is $24.5\mathrm{nautical}\mathrm{miles}$.

In unit conversion, conversion factors are used to converts the units of measure for the same quantity. Use the conversion factors to covert the distance from nautical miles to kilometers.

By using length conversion given in Appendix D, convert both miles and nautical miles into kilometers. After that, find the difference between the distances to find the difference between the two locations.

So, first of all, find both the distances in kilometers.

As given in Appendix D,

$$\begin{gathered} 1\mathrm{mile}=1.609\mathrm{km} \\ 1\mathrm{nautical}\mathrm{mile}=1.852\mathrm{km} \\ \mathrm{find}\mathrm{the}\mathrm{distance}\mathrm{in}\mathrm{miles}. \\ 24.5\mathrm{miles}=24.5\mathrm{miles}\times \frac{1.60\mathrm{km}}{1\mathrm{mile}} \\ =39.42\mathrm{km} \end{gathered}$$

Thus, $24.5\mathrm{miles}$is equivalent to$39.42\mathrm{km}$

Find the distance in nautical miles.

$$\begin{gathered} 24.5\mathrm{nautical}\mathrm{mile}=24.5\mathrm{miles}\times \frac{1.852\mathrm{km}}{1\mathrm{mile}} \\ =45.37\mathrm{km} \end{gathered}$$

Thus, $24.5\mathrm{miles}$is equivalent to$45.37\mathrm{km}$.

The difference between the distance covered in nautical miles and miles is,

$45.37-39.42=5.95\mathrm{km}$

Thus, the difference between the two distance is$5.95\mathrm{km}.$