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Chapter 1: Problem 51

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

Short Answer

Expert verified
The car's speed in miles per hour is \( 40.38 \ \mathrm{mi/h} \), which is greater than the speed limit of 40 mi/h. Therefore, the car would violate the 40 mi/h speed limit.

Step by step solution

01

Write down given values

We are given: - Car's speed: 65 km/h - Speed limit: 40 mi/h
02

Convert car's speed to miles per hour

To convert the car's speed from km/h to mi/h, we will use the conversion factor 1 km = 0.621371 mi. Car's speed in mi/h = \( 65 \ \mathrm{km/h} \times 0.621371 \ \dfrac{\mathrm{mi}}{\mathrm{km}} \)
03

Calculate car's speed in miles per hour

Multiply the car's speed in km/h by the conversion factor: Car's speed in mi/h = \( 65 \ \mathrm{km/h} \times 0.621371 \ \dfrac{\mathrm{mi}}{\mathrm{km}} = 40.38 \ \mathrm{mi/h} \)
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 (40 mi/h) to determine if it is exceeding the limit: 40.38 mi/h (Car's speed) > 40 mi/h (Speed limit)
05

Conclusion

Since the car's speed in miles per hour (40.38 mi/h) is greater than the given speed limit (40 mi/h), the car would indeed violate the 40 mi/h speed limit.

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