Problem 44 - Elementary Algebra

Question

The distance traveled \(D\) is equal to the average rate \(r\) times the time traveled \(t\) at that rate: \(D=r t .\) Determine the distance traveled given the rate and the time. 60 meters per second for 30 seconds

Step-by-Step Solution

Answer

The distance traveled is 1800 meters.

Step 1: Identify the Variables

In this problem, the rate of travel \( r \) is given as 60 meters per second and the time \( t \) is 30 seconds. We need to find the distance traveled \( D \).

Step 2: Write the Equation

The formula to find the distance traveled is \( D = r \times t \). We will use this equation to calculate the distance.

Step 3: Substitute the Values

Substitute the given values into the equation: \( D = 60 \text{ m/s} \times 30 \text{ s} \).

Step 4: Perform the Calculation

Multiply the rate and the time: \( 60 \times 30 = 1800 \). Thus, \( D = 1800 \) meters.

Key Concepts

Understanding Rate

In the context of distance, the rate is a measure of how fast something is moving. It's typically expressed as a distance traveled over a specific unit of time. In formulas, rate is often represented by the letter \( r \). The rate is crucial because it tells us the speed at which an object is moving.
Examples of rate include:

• 60 kilometers per hour (km/h)
• 40 miles per hour (mph)
• 10 meters per second (m/s)

In our problem, the rate is 60 meters per second. This means for every second, the object moves 60 meters.
Having a clear understanding of rate allows us to determine how far the object will travel over a given period of time.Remember, the unit of rate should match the other units in the calculation, like time.

Importance of Time

Time plays a key role when you're calculating distance. It represents how long the object has been moving. Without knowing the time, you cannot accurately determine how far an object has traveled.
Consider some common time units:

• Seconds (s)
• Minutes (min)
• Hours (h)

In our specific problem, time is given as 30 seconds. This means the object traveled with a constant rate for 30 seconds. Understanding time in problems like these is essential because it directly impacts the formula \( D = r \times t \). Make sure your time unit is consistent with the rate's time unit, like in our exercise where both are in seconds.

Solving the Equation

Equation solving is the process of finding an unknown value by manipulating a math equation. In the context of our exercise, we are using the simple formula for distance, which is \( D = r \times t \).
To solve this equation, follow these key steps:

• Identify what information you have: known values for rate and time.
• Plug these values into the formula.
• Conduct the necessary mathematical operations – typically multiplication here.

For example, substituting our exercise values, the multiplication looks like this: \( 60 \times 30 = 1800 \). Hence, the distance \( D \) is 1800 meters. Ensure you correctly substitute the values and do the calculations carefully to find the correct solution.