Question

The highest speed limit in the United States is \(85 \mathrm{mph}\) on an isolated stretch of rural interstate in Texas. What is the speed limit in kilometers per hour \((1 \mathrm{mi}=1609 \mathrm{~m})\) ? Report your answer as a whole number.

Short answer

The speed limit is approximately 137 km/h.

Step-by-step solution

Identify Given Data

The speed limit is \(85 \text{ mph}\). We also have the conversion factor \(1 \text{ mile} = 1609 \text{ meters}\). We need to convert the speed from miles per hour to kilometers per hour.

Convert Miles to Kilometers

First, convert the distance from miles to kilometers. We know that \(1 \text{ mile} = 1609 \text{ meters}\) and \(1 \text{ kilometer} = 1000 \text{ meters}\). Thus, \(1 \text{ mile} = \frac{1609}{1000} = 1.609 \text{ kilometers}\).

Apply Conversion to Speed

Now, use the conversion factor to convert the speed limit: \[85 \text{ mph} = 85 \times 1.609 \text{ kilometers per hour}\]

Calculate the Result

Perform the calculation: \[85 \times 1.609 = 136.765 \text{ kilometers per hour}\]. Round to the nearest whole number.

Present the Answer

After rounding, the speed limit is approximately \(137 \text{ kilometers per hour}\).

Key concepts

Miles to Kilometers

Converting miles to kilometers is a common task when dealing with distance measurements. This conversion helps when you're dealing with travel or geographical data. In unit conversion, we need a conversion factor, which is a known value. For the miles to kilometers conversion, we use:

• 1 mile = 1.609 kilometers

To convert from miles to kilometers, you simply multiply the number of miles by 1.609. So, if you have a speed limit of 85 miles per hour and want to find out what it is in kilometers per hour, the operation is:

• 85 miles/hour \( \times \) 1.609 km/mile = 136.765 km/hour

This process changes the unit from miles to kilometers, which is often necessary for international understanding and use in scientific settings.

Speed Calculation

Converting speed from one unit to another is important in physics, travel, and engineering. Speed is typically described in units of distance over time, like miles per hour (mph) or kilometers per hour (km/h). To perform the conversion of speed from mph to km/h, you can use the distance conversion factor:

• 1 mile = 1.609 kilometers

When you multiply the speed in mph by the conversion factor, you directly obtain the speed in km/h, like so:

• Speed (km/h) = Speed (mph) \( \times \) 1.609

For example, with a speed of 85 mph, you calculate:

• 85 mph \( \times \) 1.609 = 136.765 km/h

This conversion helps compare and utilize speeds in countries using different units of measurement.

Rounding Numbers

Rounding numbers is a mathematical practice for simplifying numbers while keeping their value close to what it was. This is particularly useful when you have a repeating number after a decimal point, and you want to make it easier to interpret or use. In this exercise, we have calculated a speed of 136.765 kilometers per hour, and then rounded to the nearest whole number.

• Identify the place you want to round to, such as the nearest whole number.
• Look at the digit to the right of your rounding place (6 in this case).
• If it's 5 or greater, round up. If it's 4 or less, round down.

So, 136.765 rounds to 137 because 7 is 5 or greater. Rounding can simplify communication and calculations by focusing on significant figures rather than unnecessary precision.