$$ \definecolor{crimBlue}{rgb}{0.196,0.467,0.533} \definecolor{crimOrange}{rgb}{0.969,0.553,0.149} \definecolor{crimGreen}{rgb}{0.498,0.694,0.302} $$
Sam ran 63,756 feet per 70 minutes. What is Sam's rate in miles per hour? (There are 5,280 feet in one mile.)

Step 1: What is Sam's rate as stated?

Step 2: What factor is used to convert feet per minute into miles per minute?

Step 3: What factor is used to convert miles per minute to miles per hour?

Step 4: Calculate the result:

61,776 • 60
70 • 5,280
= miles / hour
$$= \frac {63,756 \text { ft}} {70 \text { min}}$$
$$= \frac {63,756 {\color {crimOrange} \text { ft}}} {70 \text { min}}$$
$$= \frac {63,756 {\color {crimOrange} \text { ft}}} {70 {\color {crimOrange} \text { min}}}$$
$$= \frac {63,756 {\color {crimOrange} \cancel {\text { ft}}}} {70 \text { min}} \cdot \frac {1 \text { mile}} {5,280 {\color {crimOrange} \cancel { \text { ft}}}}$$
$$= \frac {63,756 {\color {crimOrange} \cancel {\text { ft}}}} {70 {\color {crimOrange} \text { min}}} \cdot \frac {1 \text { mile}} {5,280 {\color {crimOrange} \cancel { \text { ft}}}}$$
$$= \frac {63,756 {\color {crimOrange} \cancel {\text { ft}}}} {70 {\color {crimOrange} \text { min}}} \cdot \frac {1 \text { mile}} {5,280 {\color {crimOrange} \cancel { \text { ft}}}}$$
$$= \frac {63,756 {\color {crimOrange} \cancel { \text { ft}}}} {70 {\color {crimOrange} \cancel {\text { min}}}} \cdot \frac {1 \text { mile}} {5,280 {\color {crimOrange} \cancel {\text { ft}}}} \cdot \frac {60 {\color {crimOrange} \cancel {\text { min}}}} {1 \text { hr}} $$
$$= \frac {63,756 {\color {crimOrange} \cancel { \text { ft}}}} {70 {\color {crimOrange} \cancel {\text { min}}}} \cdot \frac {1 \text { mile}} {5,280 {\color {crimOrange} \cancel {\text { ft}}}} \cdot \frac {60 {\color {crimOrange} \cancel {\text { min}}}} {1 \text { hr}} $$
$$= \frac {63,756 {\color {crimOrange} \cancel { \text { ft}}}} {70 {\color {crimOrange} \cancel {\text { min}}}} \cdot \frac {1 \text { mile}} {5,280 {\color {crimOrange} \cancel {\text { ft}}}} \cdot \frac {60 {\color {crimOrange} \cancel {\text { min}}}} {1 \text { hr}} $$
$$ = 10.35 \frac {\text{miles}}{\text{hour}} $$