Question

Would a car traveling at a constant speed of \(65 \mathrm{~km} / \mathrm{h}\) violate a 40\. mi/h speed limit?

Short answer

The car traveling at a constant speed of \(65 \mathrm{~km} / \mathrm{h}\) is equivalent to approximately \(40.389 \mathrm{~mi} / \mathrm{h}\), which is greater than the speed limit of \(40 \mathrm{~mi} / \mathrm{h}\). Therefore, the car would violate the \(40 \mathrm{~mi} / \mathrm{h}\) speed limit.

Step-by-step solution

Identify the conversion factor from kilometers to miles

The conversion factor from kilometers to miles is 1 kilometer = 0.621371 miles. We can use this conversion factor to convert the car's speed from km/h to mi/h.

Set up the conversion equation

To convert the car's speed from km/h to mi/h, we can set up a proportion using the conversion factor. It should look like this: \(\frac{65 \, \mathrm{km/h}}{1} = \frac{x \, \mathrm{mi/h}}{0.621371}\) Where x is the speed of the car in mi/h.

Solve for the speed of the car in mi/h

To solve for x, we can multiply both sides of the equation by 0.621371. Doing this, we get: \(65 \, \mathrm{km/h} * 0.621371 = x \, \mathrm{mi/h}\) Now, we can find the value of x: \(x = 65 * 0.621371\) \(x \approx 40.389 \, \mathrm{mi/h}\)

Compare the car's speed to the speed limit

Now that we have the car's speed in mi/h, we can compare it to the speed limit of 40 mi/h. The car's speed is approximately 40.389 mi/h which is greater than the speed limit of 40 mi/h.

Conclusion

Since the car's speed in mi/h (40.389 mi/h) is greater than the speed limit of 40 mi/h, the car traveling at a constant speed of 65 km/h would violate the 40 mi/h speed limit.

Key concepts

Understanding Speed Calculation

When dealing with speed calculation, it's important to understand that speed is simply how fast something is moving. This is typically expressed as a distance over time, like kilometers per hour (km/h) or miles per hour (mi/h).
Let's break it down further:

• Speed tells you how far something travels in a specific period of time.
• To find speed, you can use the formula: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \).
• If you're given a speed in km/h and you need it in mi/h, or vice versa, you'll need to convert the speed to the desired unit.

This is a crucial step when checking compliance with speed limits that are usually in the local customary units.
Speed calculation helps in various practical applications, such as navigation, traffic enforcement, and travel planning.

Using a Conversion Factor

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. It acts like a bridge between two different measurement systems. When you have a conversion factor, you can accurately switch between units while maintaining the same value.
For example:

• The conversion factor between kilometers and miles is 1 kilometer equals approximately 0.621371 miles.
• To convert a speed from km/h to mi/h, you multiply the speed by this conversion factor.
• Conversely, to go from mi/h to km/h, you would divide by the same factor.

Conversion factors are essential in unit conversion tasks because they ensure you're making mathematically consistent calculations. They simplify the process of translating measurements into the units you need, whether you're working on a problem for school or figuring out travel distances.

Converting Kilometers to Miles

Converting kilometers to miles is a common requirement, especially when you are dealing with speed limits or travel distances in places where the customary unit differs from kilometers.
Here's how you can do it:

• Start with the speed or distance value in kilometers.
• Multiply this value by the conversion factor 0.621371 to get the equivalent value in miles.

For example, converting a speed of 65 km/h:
The calculation is straightforward: \( 65 \times 0.621371 = 40.389 \, \text{mi/h} \).
Whenever you convert units, remember:

• Cross-verify your calculations to ensure accuracy.
• Understand that these mathematical conversions allow you to adapt to different measurement systems effortlessly.

This knowledge is particularly useful in contexts where varying unit systems are used, like global travel or international settings.