Problem 54 - Prealgebra

Question

December and January are the best times for traveling in a hot-air balloon because the jet streams in the Northern Hemisphere are the strongest. They reach speeds of 400 kilometers per hour. Convert this to miles per hour by dividing by 1.61. Round to the nearest whole number.

Step-by-Step Solution

Answer

The speed is approximately 248 mph.

Step 1: Identify Given Information

We are given the speed in kilometers per hour (km/h) as 400 km/h and need to convert it to miles per hour (mph).

Step 2: Recall the Conversion Factor

The exercise states that to convert kilometers to miles, we divide by 1.61. Therefore, the conversion factor is 1 kilometer = 1/1.61 miles.

Step 3: Perform the Conversion

To convert 400 km/h to mph, use the conversion formula: \[ \text{Speed in mph} = \frac{\text{Speed in km/h}}{1.61} \] Substitute the given speed: \[ \text{Speed in mph} = \frac{400}{1.61} \approx 248.447 \]

Step 4: Round to the Nearest Whole Number

The computed speed is approximately 248.447 mph. To round to the nearest whole number, consider the decimal part. Since 0.447 is less than 0.5, round down to 248 mph.

Key Concepts

Kilometers to Miles

When traveling, especially in regions where different units of measurement are used, it's crucial to understand how to convert between these units. One common conversion is from kilometers to miles.
In this context, we're dealing with speed, so to convert from kilometers per hour (km/h) to miles per hour (mph), we'll use a conversion factor that accounts for the difference in distance units between kilometers and miles.

• 1 kilometer is approximately 0.621 miles.
• The common conversion factor used is dividing the number of kilometers by 1.61 to get miles.

This factor comes from dividing 1 km by the approximate value of miles equivalent to one kilometer, which is why we divide 400 km/h by 1.61 to find its equivalent speed in mph. This approach is straightforward, as it provides the miles figure by essentially scaling down the kilometers figure by the fractional distance measure difference between kilometers and miles.

Rounding Numbers

In mathematics and everyday life, rounding numbers helps simplify calculations and make them easier to understand or communicate. The rounding process involves reducing the number of digits after the decimal point, usually to make a number easier to work with or more compatible with real-world scenarios.
Let's take a closer look at how to round numbers:

• Identify the decimal digit at the position you want to round to. Here, it's rounding to the nearest whole number.
• Look at the next digit to the right (this is the deciding digit).
• If the deciding digit is 5 or more, you round up the last remaining digit.
• If the deciding digit is less than 5, you round down.

In our exercise, we found 248.447 when converting km/h to mph. The decimal 0.447 is less than 0.5, so we round down to 248 mph.

Speed Conversion

Understanding speed conversion is important for comprehending how fast an object is moving under different measurement units. When you've got a speed in one unit and need it in another, knowing how to convert accurately ensures you're correctly interpreting information.
Speed conversion isn't just a simple formula – it's about understanding how these units relate to each other and applying the conversion systematically.

• Identify the original speed and its unit (e.g., km/h).
• Utilize the correct conversion factor to switch units (e.g., dividing by 1.61 to convert km/h to mph).

Once converted, rounding may be necessary to make the result more practical, as seen in our example. This ensures the speed is in a form that is common or expected, like whole numbers in many real-life travel speeds.