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Chapter 1: Problem 49

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

Short Answer

Expert verified
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

01

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.
02

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.
03

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: \(x = 65 * 0.621371\) \(x \approx 40.389 \, \mathrm{mi/h}\)
04

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.
05

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.

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