Problem 39 - Algebra 1: Concepts and Skills

Question

Find the distance traveled using \(d=r t\). A person walks at a rate of 4 feet per second for 1 minute.

Step-by-Step Solution

Answer

The person traveled a distance of 240 feet.

Step 1: Convert minutes to seconds

1 minute is equivalent to 60 seconds. This is because there are 60 seconds in a minute.

Step 2: Substitute the values into the formula

Now that we have converted the time to seconds, we can substitute the values for the rate \(r\) and time \(t\) into the distance formula \(d = rt\). Doing so gives us \(d = 4 feet/second * 60 seconds\).

Step 3: Calculate the distance

Multiplying 4 feet per second by 60 seconds results in 240 feet. So the distance \(d\) traveled is 240 feet.

Key Concepts

Understanding Rate and Time

The concept of rate and time is essential in calculating how far someone or something travels within a specific period. Rate refers to how fast an entity moves. It is usually expressed in units of distance over time, such as feet per second or miles per hour. Time is simply the duration spent moving at that rate.
In this context, we calculated the distance traveled by a person walking at a rate of 4 feet per second. Using the distance formula, which is expressed as \(d = rt\), helps us understand the relationship between rate, time, and distance. Here, \(r\) represents the rate and \(t\) is the time.
By multiplying these two variables, you can find the total distance covered. Remember that the consistency between the units of rate and time is crucial to avoid any confusion during calculations.

Importance of Unit Conversion

Unit conversion is the process of changing one unit of measure to another to maintain consistency in calculations. In our problem, we began with a time measurement in minutes, whereas the rate was given in feet per second.

• To ensure both time and rate use compatible units, we converted minutes to seconds.
• 1 minute equals 60 seconds, so the time was converted straightforwardly by multiplying 1 by 60.

Being consistent with units helps prevent errors and makes it easier to apply the distance formula accurately. Converting units is a common step when dealing with rate and time calculations since rates are often provided in units per second, minute, or hour. Always check your units at the initiation of calculations to avoid mistakes.

How to Calculate Distance Using the Formula

Distance calculation is at the heart of solving this type of problem. Once the rate and time are compatible in terms of units, you can apply the distance formula \(d = rt\).
This formula is simple yet powerful; it tells us that distance (\(d\)) is the product of rate (\(r\)) and time (\(t\)).

• Substituting the values for our specific case: \(d = 4 \text{ feet/second} \times 60 \text{ seconds}\).
• The multiplication here simplifies to calculate the total distance traveled as 240 feet.

Being familiar with the formula and ensuring all quantities are in appropriate units will lead to a correct and easily understandable solution. This fundamental relationship between distance, rate, and time appears across many real-world applications, making it a key concept to master.