A train moves at a constant rate. The table and graph below show the relationship between the time, in hours, since the train left its station, and the distance, in miles, that it has traveled. What is the rate of change of the number of miles the train travels per hour? Solve on paper, and then enter your answer on Zearn. 4) 8 Time in hours, x Distance in miles, y 0.5 42 1.5 2.5 The rate of change is 126 210 miles per hour. Distance in miles 420 378 336 294- 252 210- 168 126 84 42 0 0.5 1 1.5 2 2.5 3 Time in hours 3.5 4 4.5 5 Enter ✔
A train moves at a constant rate. The table and graph below show the relationship between the time, in hours, since the train left its station, and the distance, in miles, that it has traveled. What is the rate of change of the number of miles the train travels per hour? Solve on paper, and then enter your answer on Zearn. 4) 8 Time in hours, x Distance in miles, y 0.5 42 1.5 2.5 The rate of change is 126 210 miles per hour. Distance in miles 420 378 336 294- 252 210- 168 126 84 42 0 0.5 1 1.5 2 2.5 3 Time in hours 3.5 4 4.5 5 Enter ✔
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Constant Rate of Movement of a Train
#### Overview:
A train moves at a constant rate. This educational content explores the relationship between time, in hours, since the train left its station, and the distance, in miles, that it has traveled.
#### Task:
Calculate the rate of change (speed) of the train in miles per hour. Work this out on paper, then enter your answer on the educational platform.
#### Table:
The table below displays the time in hours (\(x\)) and the corresponding distance in miles (\(y\)) covered by the train:
| Time in hours (\(x\)) | Distance in miles (\(y\)) |
|-----------------------|---------------------------|
| 0.5 | 42 |
| 1.5 | 126 |
| 2.5 | 210 |
#### Graph:
A graph is provided on the right:
- **X-axis**: Represents time in hours.
- **Y-axis**: Represents distance in miles.
- The graph shows a straight line passing through the points (0.5, 42), (1.5, 126), and (2.5, 210), illustrating the linear relationship between time and distance.
The linearity of the graph indicates a constant rate of speed.
#### Calculation:
The rate of change is represented as the slope of the line on the graph:
\[
\text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{126 - 42}{1.5 - 0.5} = \frac{84}{1} = 84 \text{ miles per hour}
\]
\[
\text{Rate of change} = \frac{210 - 126}{2.5 - 1.5} = \frac{84}{1} = 84 \text{ miles per hour}
\]
The train travels at a rate of \(84\) miles per hour.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd5c2cde-8895-43a3-8db4-0ce93c5f2f01%2Fbe83b4bb-fac0-41b9-9c4c-4c44282fef0f%2Futg784_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Constant Rate of Movement of a Train
#### Overview:
A train moves at a constant rate. This educational content explores the relationship between time, in hours, since the train left its station, and the distance, in miles, that it has traveled.
#### Task:
Calculate the rate of change (speed) of the train in miles per hour. Work this out on paper, then enter your answer on the educational platform.
#### Table:
The table below displays the time in hours (\(x\)) and the corresponding distance in miles (\(y\)) covered by the train:
| Time in hours (\(x\)) | Distance in miles (\(y\)) |
|-----------------------|---------------------------|
| 0.5 | 42 |
| 1.5 | 126 |
| 2.5 | 210 |
#### Graph:
A graph is provided on the right:
- **X-axis**: Represents time in hours.
- **Y-axis**: Represents distance in miles.
- The graph shows a straight line passing through the points (0.5, 42), (1.5, 126), and (2.5, 210), illustrating the linear relationship between time and distance.
The linearity of the graph indicates a constant rate of speed.
#### Calculation:
The rate of change is represented as the slope of the line on the graph:
\[
\text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{126 - 42}{1.5 - 0.5} = \frac{84}{1} = 84 \text{ miles per hour}
\]
\[
\text{Rate of change} = \frac{210 - 126}{2.5 - 1.5} = \frac{84}{1} = 84 \text{ miles per hour}
\]
The train travels at a rate of \(84\) miles per hour.
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