Question:
An airliner travels 15 miles in 2 minutes. What is its speed in miles per hour?
Given:
[tex] \textsf{Distance or d} = 15\ \textsf{miles} [/tex]
[tex] \textsf{Time or t} = 2\ \textsf{minutes} [/tex]
Solution:
[tex] \displaystyle \textsf{Speed} = \frac{\textsf{Distance}}{\textsf{Time}} [/tex]
[tex] \displaystyle \textsf{V} = \frac{\textsf{d}}{\textsf{t}} [/tex]
[tex] \displaystyle \textsf{V} = \frac{15\textsf{ miles}}{2\textsf{ minutes}} [/tex]
Convert miles/minutes to miles/hour:
[tex] \displaystyle \textsf{V} = \frac{15\textsf{ miles}}{2\textsf{ minutes}} \cdot \frac{1\textsf{ minute}}{\frac{1}{60}\textsf{ hour}} [/tex]
[tex] \displaystyle \textsf{V} = \frac{15\textsf{ miles} \cdot 1\textsf{ minute}}{2\textsf{ minutes} \cdot \frac{1}{60}\textsf{ hour}} [/tex]
[tex] \displaystyle \textsf{V} = \frac{15\textsf{ miles}}{\frac{2}{60}\textsf{ hour}} [/tex]
[tex] \displaystyle \textsf{V} = 15\textsf{ miles} \cdot \frac{60}{2}\frac{1}{\textsf{ hour}}[/tex]
[tex] \displaystyle \textsf{V} = 15\textsf{ miles} \cdot 30\frac{1}{\textsf{ hour}}[/tex]
[tex] \displaystyle \textsf{V} = 450\frac{ \textsf{miles}}{\textsf{ hour}}[/tex]
Answer:
[tex] \displaystyle 450\frac{ \textsf{miles}}{\textsf{ hour}}[/tex]