Question

The highest speed limit in the United States is \(85 \mathrm{mph}\) on an isolated stretch of rural interstate in Texas. What is the speed limit in kilometers per hour \((1 \mathrm{mi}=1609 \mathrm{~m})\) ? Report your answer as a whole number.

Short answer

The speed limit is 137 km/h.

Step-by-step solution

Understanding the Conversion Ratio

To find the speed limit in kilometers per hour (km/h), we need to convert miles per hour (mph) to kilometers per hour. We know that 1 mile is equal to 1609 meters.

Converting Miles to Kilometers

Since 1 mile is equal to 1609 meters, we first convert meters to kilometers by dividing by 1000 (since there are 1000 meters in a kilometer). Thus, 1 mile is equal to \( \frac{1609}{1000} = 1.609 \) kilometers.

Applying the Conversion to Speed Limit

To find the speed limit in km/h, multiply the speed limit in mph by the conversion factor from miles to kilometers. So, \( 85 \mathrm{mph} \times 1.609 \mathrm{~km/mi} \).

Calculating the Result

Perform the multiplication: \( 85 \times 1.609 = 136.765 \mathrm{~km/h} \). To report the answer as a whole number, round 136.765 to the nearest whole number, which is 137 km/h.

Key concepts

Miles to Kilometers

Converting distances from miles to kilometers is essential, particularly in domains like transportation and travel planning. Understanding how to do this conversion can make navigating between the imperial and metric systems more intuitive.
To convert miles to kilometers, we utilize the knowledge that 1 mile equals 1609 meters. Since there are 1000 meters in a kilometer, each mile converts to 1.609 kilometers. This conversion factor simplifies changing any mileage into kilometers by a simple multiplication process.
For example, if you're converting 85 miles (a typical speed limit) into kilometers, you multiply 85 by 1.609, resulting in approximately 136.77 kilometers. This precise knowledge of conversion supports accuracy in scientific and everyday applications.

Speed Conversion

Speed conversion is a necessary skill for understanding how different measurement systems reflect velocity. It often utilizes the conversion of distances, from miles to kilometers, and integrates time units such as hours.
To convert a speed limit from miles per hour to kilometers per hour, use the conversion factor from miles to kilometers. Multiply the speed in mph by the conversion factor (1.609 km/mi). For instance, converting 85 mph involves multiplying 85 by 1.609, converting it to 136.77 km/h. In many contexts, rounding provides a cleaner result, so it’s common to present this as approximately 137 km/h.
Understanding this conversion is vital, especially for international travel or when interpreting international regulations, where speed limits are commonly listed in km/h.

Metric System

The metric system is a decimal-based system of measurement used worldwide in science and by most countries for everyday purposes. Its beauty lies in its simplicity and universality, promoting a standardized approach to measurement.
Key metric units include meters for length, kilograms for mass, and liters for volume, with prefixes (like kilo-) indicating the scale. For distances, 1 kilometer is 1000 meters, and for speeds, kilometer per hour (km/h) is a common metric unit.

• Easier calculations due to its base-10 nature.
• Globally recognized standard.
• Facilitates international scientific and cooperative endeavors.

Understanding and applying the metric system simplifies conversions, such as turning miles into kilometers, fostering seamless interactions across global systems.

Mathematical Calculation

Performing mathematical calculations for conversions involves understanding the relevant factors and applying them accurately. These calculations are essential in fields such as physics, engineering, and daily life scenarios like traveling.
The process typically involves identifying the conversion ratio (for example, 1 mile equals 1.609 kilometers) and utilizing it logically. In our example, the speed limit conversion requires multiplying the given miles per hour by this ratio. This operation demands precision to ensure accuracy, rounded where appropriate, such as presenting 136.77 km/h as 137 km/h.
For success in mathematical calculations:

• Understand the units involved.
• Apply correct conversion factors.
• Use rounding to simplify results appropriately.

Mastery of these basic calculation techniques streamlines the conversion process and enhances numeric fluency.