- Identify the total distance covered at \(t=10\) minutes as \(20\) miles from the table.
- Identify the total distance covered at \(t=15\) minutes as \(30\) miles from the table.
- Calculate the difference in distance between these two time points: \(30 - 20 = 10\) miles.
- Conclude that Bob traveled \(\boxed{10 \text{ miles}}\) between 10 minutes and 15 minutes.
Explanation
- Analyzing the Data Points
To describe the distance traveled by Bob between 10 minutes and 15 minutes, we first examine the provided data table, which lists the cumulative distance covered by Bob over time. According to the table:
- At \(t = 10\) minutes, the cumulative distance covered is \(20\) miles.
- At \(t = 15\) minutes, the cumulative distance covered is \(30\) miles.
- Calculating the Distance Traveled
To determine the distance traveled specifically during the 5-minute interval between \(10\) and \(15\) minutes, we calculate the difference between the total distance at \(15\) minutes and the total distance at \(10\) minutes:
\[\Delta d = d(15) - d(10) = 30 \text{ miles} - 20 \text{ miles} = 10 \text{ miles}.\]
This confirms that Bob traveled \(10\) miles in the time interval from \(10\) to \(15\) minutes.
Examples
In real life, understanding how to read data from a table is crucial for interpreting trends, such as tracking progress on a trip or monitoring growth. For example, if you are tracking your physical activity, reading distance intervals helps you identify your pace. By identifying your position at different time markers, you can calculate the distance covered during specific segments of your journey, helping you assess your speed or time efficiency for each part of your trip.