There are 5280 feet in a mile and 3600 seconds in an hour. So, 8 feet per second is equivalent to (8 feet/second) * (1 mile/5280 feet) * (3600 seconds/1 hour) = 8 * 3600 / 5280 miles per hour.
The Correct Answer and Explanation is:
To convert 8 feet per second to miles per hour, use the following conversion: 8 feet/second×(1 mile5280 feet)×(3600 seconds1 hour)8 \, \text{feet/second} \times \left(\frac{1 \, \text{mile}}{5280 \, \text{feet}}\right) \times \left(\frac{3600 \, \text{seconds}}{1 \, \text{hour}}\right)
Step-by-step: =8×36005280 miles/hour= \frac{8 \times 3600}{5280} \, \text{miles/hour} =288005280 miles/hour= \frac{28800}{5280} \, \text{miles/hour} ≈5.45 miles/hour\approx 5.45 \, \text{miles/hour}
Final Answer:
8 feet per second is approximately 5.45 miles per hour.
Explanation
Unit conversions are essential in math, science, and everyday applications. Here, we are converting a speed given in feet per second (ft/s) into miles per hour (mph).
The key to solving this is recognizing the relationships between the units:
- There are 5280 feet in one mile.
- There are 3600 seconds in one hour.
So to go from feet to miles, we divide by 5280. To go from seconds to hours, we multiply by 3600. This keeps the physical quantity (speed) the same but changes the units.
Starting with the given speed: 8 ft/s8 \, \text{ft/s}
First, convert the feet to miles: 8 ft/s×(1 mile5280 ft)8 \, \text{ft/s} \times \left(\frac{1 \, \text{mile}}{5280 \, \text{ft}}\right)
This gives us miles per second. Now, convert seconds to hours: (85280 miles/second)×3600 seconds/hour\left(\frac{8}{5280} \, \text{miles/second}\right) \times 3600 \, \text{seconds/hour}
Multiply the numerators and divide: 8×36005280=288005280≈5.45 mph\frac{8 \times 3600}{5280} = \frac{28800}{5280} \approx 5.45 \, \text{mph}
This means that someone moving at 8 ft/s is traveling at about 5.45 mph — slightly faster than a brisk walking pace.
Understanding how to convert units using proportional reasoning like this is critical in interpreting real-world measurements, whether for speed, distance, or time.
