Question

One mile is about 1.6 kilometers. a. Which is the greater distance, 1 mile or 1 kilometer? b. Los Angeles and New York City are about 2,460 miles apart. How many kilometers apart are they? c. If the speed limit on a road in Canada is 50 kilometers per hour, what is the speed limit in miles per hour? d. In Investigation \(2,\) you learned that lightning is 1 mile away for every 5 seconds you count between the lightning and the following clap of thunder. About how many seconds would it take you to hear the thunder if the lightning were 1 kilometer away?

Short answer

1 mile; 3,936 kilometers; 31.25 miles per hour; about 3.125 seconds

Step-by-step solution

Comparing distances in part (a)

To determine which is the greater distance between 1 mile and 1 kilometer, note that 1 mile is about 1.6 kilometers. Therefore, 1 mile is greater than 1 kilometer.

Converting distance in part (b)

To convert the distance from miles to kilometers, multiply the distance in miles by the conversion factor, which is approximately 1.6: \[ 2,460 \text{ miles} \times 1.6 \frac{\text{km}}{\text{mile}} = 3,936 \text{ km} \]

Converting speed limit in part (c)

To convert the speed limit from kilometers per hour to miles per hour, use the inverse of the conversion factor: \[ 50 \text{ km/h} \times \frac{1 \text{ mile}}{1.6 \text{ km}} = 31.25 \text{ miles per hour} \]

Converting lightning distance to time in part (d)

To find out how many seconds it takes to hear thunder if lightning is 1 kilometer away, use the given fact that 1 mile away corresponds to 5 seconds: Since 1 mile is 1.6 kilometers, 1 kilometer is about \( \frac{1}{1.6} = 0.625 \text{ miles} \times 5 \text{ seconds per mile} = 3.125 \text{ seconds} \).

Key concepts

miles to kilometers conversion

To understand miles to kilometers conversion, it's essential to know the exact relationship between these units. One mile is approximately equal to 1.6 kilometers. This conversion factor allows us to convert miles into kilometers easily.
For example, if you want to convert 5 miles into kilometers, you multiply 5 by 1.6:

• 5 miles × 1.6 km/mile = 8 kilometers

This process provides a straightforward way to compare and convert these distances.

speed limit conversion

Converting speed limits from kilometers per hour (km/h) to miles per hour (mph) is essential for understanding speed regulations in different countries. To do this, use the inverse of the miles to kilometers conversion. In other words, 1 kilometer is approximately equal to 0.625 miles.
For example, if the speed limit is 80 km/h, you can convert it to miles per hour by multiplying 80 by the conversion factor:

• 80 km/h × 0.625 miles/km = 50 mph

Understanding this conversion can help you adjust to different speed limits when traveling.

lightning distance calculation

Calculating the distance of lightning involves understanding the time it takes for the sound of thunder to reach you. You learned that if the sound takes 5 seconds to reach you, the lightning is 1 mile away. To convert this to kilometers, recall that 1 mile is about 1.6 kilometers. Therefore, to find how many seconds it takes to hear thunder from 1 kilometer away:

• 1 kilometer ≈ 0.625 miles
• If 5 seconds corresponds to 1 mile, then 0.625 miles corresponds to:
  0.625 × 5 seconds = 3.125 seconds

Hence, it would take around 3.125 seconds to hear the thunder if the lightning were 1 kilometer away.

unit conversion in math

Unit conversion in math is a fundamental skill that involves converting one unit of measure into another. This is done using conversion factors, which are ratios that express how many of one unit are equal to another unit. For instance, if you know that 1 mile is approximately 1.6 kilometers, you can easily convert:

• Distances: miles to kilometers and vice versa
• Speeds: km/h to mph and vice versa

A solid understanding of unit conversions is crucial not only for math problems but also for real-life scenarios like traveling, cooking, and understanding scientific data.