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Converting Units of Rates

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]\[
\frac{63,756 \text{ ft}}{5,280 \text{ ft/mi}} = 12.08 \text{ mi}
\][/tex]

Step 2: Convert minutes to hours.
[tex]\[
\frac{70 \text{ min}}{60 \text{ min/hr}} = 1.167 \text{ hr}
\][/tex]

Step 3: Calculate the rate in miles per hour.
[tex]\[
\frac{12.08 \text{ mi}}{1.167 \text{ hr}} = 10.35 \text{ mi/hr}
\][/tex]

Therefore, Sam's rate is approximately 10.35 miles per hour.

Sagot :

GinnyAnswer
Sure, let's go through the solution step-by-step.

Step 1: Calculate Sam's rate in feet per minute.

Sam runs 63,756 feet in 70 minutes. To find the rate in feet per minute, divide the total distance by the total time in minutes:
[tex]\[ \text{Rate in feet per minute} = \frac{63,756 \text{ feet}}{70 \text{ minutes}} = 910.8 \text{ feet per minute} \][/tex]

Step 2: Convert feet per minute to miles per minute.

Since there are 5,280 feet in a mile, we need to convert the rate from feet per minute to miles per minute:
[tex]\[ \text{Rate in miles per minute} = \frac{910.8 \text{ feet per minute}}{5,280 \text{ feet per mile}} = 0.1725 \text{ miles per minute} \][/tex]

Step 3: Convert miles per minute to miles per hour.

There are 60 minutes in an hour. To convert the rate from miles per minute to miles per hour, multiply by 60:
[tex]\[ \text{Rate in miles per hour} = 0.1725 \text{ miles per minute} \times 60 \text{ minutes per hour} = 10.35 \text{ miles per hour} \][/tex]

Summary:

The calculations lead us to conclude that Sam's running rate is:
- 910.8 feet per minute
- 0.1725 miles per minute
- 10.35 miles per hour

Therefore, Sam's rate is 10.35 miles per hour.
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