- Identify that the speed is in miles per second and the time is in minutes.
- Convert the lesson duration from minutes to seconds: \(45 \times 60 = 2700\).
- Apply the distance formula \(d = v \times t\), resulting in \((1.9 \times 10^5) \times 2700\).
- Select the option: \(\boxed{1.9 \times 10^5 \text{ multiplied by } 2700}\).
Explanation
- Analyzing the Units and Data
To calculate the distance traveled by light, we must first ensure our units are consistent. The speed of light is given as \(1.9 \times 10^5\) miles per second, while the duration of the lesson is provided in minutes. Since the speed is expressed in miles per second, we must convert the duration of the lesson into seconds.
- Converting Time to Seconds
We know that there are \(60\) seconds in \(1\) minute. To find the total number of seconds in a \(45\)-minute lesson, we multiply the number of minutes by the number of seconds per minute:
\[t_{sec} = 45 \text{ minutes} \times 60 \text{ seconds/minute} = 2700 \text{ seconds}.\]
- Calculating the Total Distance
The relationship between distance, speed, and time is given by the formula:
\[d = v \times t\]
where \(d\) is the distance, \(v\) is the speed, and \(t\) is the time in the appropriate units. Substituting our values:
\[v = 1.9 \times 10^5 \text{ miles/second}\]
\[t = 2700 \text{ seconds}\]
The total distance is therefore the product of these two values:
\[d = (1.9 \times 10^5) \times 2700 \text{ miles}.\]
- Conclusion and Selection
Comparing our derived expression, \((1.9 \times 10^5) \times 2700\), with the given choices, we identify the correct option as:
\[\boxed{1.9 \times 10^5 \text{ multiplied by } 2700}.\]
Examples
Understanding how to convert units is essential in fields like physics and engineering, where data often arrives in different scales. For example, if you are designing a communication network, you might need to calculate how long it takes for a signal to travel across a country at light speed. Converting minutes to seconds ensures your calculations align with the speed of signals, preventing errors that could lead to signal lag or synchronization issues in your network design.