Question

don took his family on a road trip to canada. when he arrived, he noticed the speed limits were posted in kilometers per hour. dons car displays speed in miles per hour.

if the posted speed limit is 100 km per hour, how fast can don drive in miles per hour, rounded to the nearest tenth?

(note: 1 mi = 1.60934 km)

a. 160.9 mi/hr
b. 62.1 mi/hr
c. 98.4 mi/hr
d. 101.6 mi/hr

Explanation:

🆕 New Concept Discovered: Unit Conversion and Dimensional Analysis
Converting measurements between different systems of units.

Step 1: Identify the given values and conversion factor

We need to convert a speed of \( 100\text{ km/h} \) into miles per hour (\(\text{mi/h}\)).

The conversion factor provided is:

$$ 1\text{ mi} = 1.60934\text{ km} $$

This means we can write the conversion ratio as:

$$ \frac{1\text{ mi}}{1.60934\text{ km}} $$

Step 2: Set up the conversion equation

To convert kilometers to miles, we multiply the given speed by the conversion ratio so that the kilometer units cancel out:

$$ \text{Speed in mi/h} = 100\text{ km/h} \times \frac{1\text{ mi}}{1.60934\text{ km}} $$

$$ \text{Speed in mi/h} = \frac{100}{1.60934}\text{ mi/h} $$

Step 3: Calculate and round the result

Perform the division:

$$ \frac{100}{1.60934} \approx 62.1371\text{ mi/h} $$

Rounding to the nearest tenth gives:

$$ 62.1\text{ mi/h} $$

This matches option B.

Answer:

B. \( 62.1\text{ mi/h} \)