# Conversion Factors

Imagine a question about average speed…take a sailboat race that spans 750 miles and is completed in 3 days, 20 hrs and 13 minutes. What is the average speed of this boat in miles per hour?

Conversion factors are very helpful in questions like this, along the same lines as dimensional analysis that is often used in chemistry.

First, convert the time to hours:

$\left( 3\quad days\times \frac { 24\quad hrs }{ 1\quad day } \right) +\left( 20\quad hrs \right) +\left( 13\quad min\times \frac { 1\quad hr }{ 60\quad min } \right) =92.22\quad hrs\quad$

We use conversion factors because they help us convert multiple types of units. Here, I have deleted the units that cancel.

$\left( 3\quad \times \quad 24\quad hrs \right) +\quad \left( 20\quad hrs \right) +\left( 13\quad \times \frac { 1\quad hr }{ 60 } \right) =92.22\quad hrs\quad$

Finally, $\frac { 750\quad miles }{ 92.2\quad hours } =\quad 8.13\quad mph$