Convert 3.409 miles per hour into km per minute.
The correct answer and explanation is :
To convert 3.409 miles per hour (mph) into kilometers per minute (km/min), follow these steps:
Step 1: Convert miles to kilometers
We use the conversion factor:
[
1 \text{ mile} = 1.60934 \text{ kilometers}
]
Thus,
[
3.409 \times 1.60934 = 5.485 \text{ km per hour}
]
Step 2: Convert hours to minutes
Since there are 60 minutes in an hour, we divide by 60:
[
\frac{5.485}{60} = 0.09142 \text{ km/min}
]
Final Answer:
[
\mathbf{0.09142} \text{ km/min}
]
Explanation (300 words)
The key to this conversion is understanding unit relationships. Speed is typically measured in miles per hour or kilometers per hour, but different contexts may require other units, such as kilometers per minute.
We start by converting miles per hour (mph) to kilometers per hour (km/h) because the metric system uses kilometers. The standard conversion factor between miles and kilometers is 1 mile = 1.60934 km. Multiplying 3.409 miles by 1.60934 gives the equivalent distance in kilometers per hour.
Next, since speed is given in terms of per hour, we must express it in terms of per minute. Since 1 hour contains 60 minutes, we divide the kilometer-per-hour value by 60 to get the kilometer-per-minute value.
Mathematically, the entire conversion is:
[
3.409 \times 1.60934 \div 60 = 0.09142 \text{ km/min}
]
This process ensures that units are properly canceled and converted correctly.
This method is useful in real-life applications such as running, cycling, or vehicle speed adjustments. If a person or object moves at 3.409 mph, knowing that it translates to 0.09142 km per minute helps in various calculations where speed is required in metric units rather than imperial.
Thus, the final converted speed is 0.09142 km/min, which is the correct and precise answer.