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?

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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