Problem 43 - Prealgebra

Question

Speed limit. The maximum speed limit on part of Highway 101 in California is 55 miles/hour. Convert 55 miles/hour to feet/second. (Round to the nearest tenth.)

Step-by-Step Solution

Answer

55 miles/hour is approximately 80.7 feet/second.

Step 1: Understand Units and Conversion Factors

The problem asks us to convert a speed from miles per hour to feet per second. To do this, we need to know the conversion factors: 1 mile = 5280 feet and 1 hour = 3600 seconds.

Step 2: Convert Miles to Feet

Convert the speed from miles per hour to feet per hour by multiplying by the number of feet in a mile. This gives: \[55 \text{ miles/hour} \times 5280 \text{ feet/mile} = 290400 \text{ feet/hour}.\]

Step 3: Convert Hours to Seconds

Next, we convert feet per hour to feet per second by dividing by the number of seconds in an hour:\[290400 \text{ feet/hour} \div 3600 \text{ seconds/hour} = 80.6667 \text{ feet/second}.\]

Step 4: Round the Result

Finally, round the result to the nearest tenth to find the final answer is approximately:\[80.7 \text{ feet/second}.\]

Key Concepts

Speed Conversion

Speed conversion is a fundamental concept in mathematics and physics that allows us to understand how quickly something is moving by converting it into different units. It's essential when comparing speeds given in various systems of measurement. For instance, it's common to convert units like miles per hour (mph) into meters per second (m/s) or feet per second (ft/s). This process involves using specific conversion factors that relate one unit of measurement to another.

• When performing speed conversion, the key is to understand the value of one unit in terms of another. For example, knowing that 1 mile is equivalent to 5280 feet is crucial for converting between these units.
• Additionally, being aware of time conversions, such as the fact that 1 hour equals 3600 seconds, allows for the complete transformation from miles per hour to a speed in feet per second.

By combining these conversion factors properly, you can achieve an accurate transformation between different speed units. This skill is particularly useful in real-world applications, such as adjusting speeds from road signs that differ based on country or region.

Miles per Hour to Feet per Second

Converting from miles per hour to feet per second is a common exercise in speed conversion problems. The process involves using two key conversion factors:

• Convert miles to feet: Recognize that there are 5280 feet in a mile. This means that if you have a certain number of miles, you can multiply it by 5280 to find out how many feet that distance represents.
• Convert hours to seconds: Understand that 1 hour is equal to 3600 seconds. When dealing with speed, which is often given in miles per hour, you will need to account for the time conversion to express the speed in feet per second.

Once you have both conversion factors in place, the process becomes straightforward. First, convert the speed from miles per hour to feet per hour by multiplying. Then, convert that result to feet per second by dividing by the number of seconds in an hour.
This step-by-step process ensures that each component of the conversion is carried out accurately, leading to a reliable final result.

Rounding Numbers

Rounding numbers is a mathematical technique used to simplify numbers, making them easier to read and work with. In many cases, especially in conversion problems, the exact decimal representation can be less useful or practical than a rounded figure.

• Understanding rounding: When rounding to the nearest tenth, look at the digit in the hundredths place. If that digit is 5 or greater, you round the number in the tenths place up by one. If it is less than 5, you leave the number in the tenths place as it is.
• Applying in conversions: After converting a speed or any measurement, you may arrive at a decimal value, such as 80.6667. Rounding this to the nearest tenth involves checking the digit in the hundredths place (6 in this case), which means rounding up the tenths place, giving you 80.7.

This method is prevalent in many fields, from scientific calculations where precision is critical, to more everyday settings where approximate values are adequate, such as estimating travel times.