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Sam ran 63,756 feet in 70 minutes. What is Sam's rate in miles per hour? (There are 5,280 feet in one mile.)

Step 1: Convert feet to miles.
[tex]\[
\frac{63,756 \text{ ft}}{5,280 \text{ ft/mi}} = \text{miles}
\][/tex]

Step 2: Convert minutes to hours.
[tex]\[
\frac{70 \text{ minutes}}{60 \text{ minutes/hour}} = \text{hours}
\][/tex]

Step 3: Calculate the rate in miles per hour.
[tex]\[
\frac{63,756 \text{ ft} \cdot 60}{70 \cdot 5,280} = \square \text{ miles/hour}
\][/tex]

Step 4: Simplify the expression.
[tex]\[
\frac{63,756 \text{ ft}}{70 \text{ min}} = \text{rate in feet per minute}
\][/tex]
[tex]\[
\frac{63,756 \text{ ft}}{70 \text{ min}} \cdot \frac{1 \text{ mi}}{5,280 \text{ ft}} = \text{rate in miles per minute}
\][/tex]
[tex]\[
\frac{63,756 \text{ ft}}{70 \text{ min}} \cdot \frac{1 \text{ mi}}{5,280 \text{ ft}} \cdot \frac{60 \text{ min}}{1 \text{ hr}} = \text{rate in miles per hour}
\][/tex]



Answer :

GinnyAnswer
To solve the problem of finding Sam's running rate in miles per hour, we can follow a step-by-step approach. Here’s the detailed solution:

### Step 1: Convert Feet to Miles
First, we need to convert the distance Sam ran from feet to miles. We know that there are 5,280 feet in one mile. Thus, we use the conversion factor [tex]\( \frac{1 \text{ mile}}{5280 \text{ feet}} \)[/tex]:

[tex]\[ \text{Distance in miles} = \frac{63,756 \text{ feet}}{5,280 \text{ feet/mile}} = 12.075 \text{ miles} \][/tex]

### Step 2: Convert Minutes to Hours
Next, we need to convert the time from minutes to hours. There are 60 minutes in one hour, so we can use the conversion factor [tex]\( \frac{1 \text{ hour}}{60 \text{ minutes}} \)[/tex]:

[tex]\[ \text{Time in hours} = \frac{70 \text{ minutes}}{60 \text{ minutes/hour}} = 1.1666666666666667 \text{ hours} \][/tex]

### Step 3: Calculate the Rate in Miles per Hour
Finally, to find Sam’s rate in miles per hour, we divide the distance in miles by the time in hours:

[tex]\[ \text{Rate} = \frac{12.075 \text{ miles}}{1.1666666666666667 \text{ hours}} = 10.35 \text{ miles per hour} \][/tex]

Hence, the detailed solution confirms that Sam's running rate is 10.35 miles per hour.

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