Question
Janet and her friend Molly ran in the Chasetown City-View Race. Janet finished the race in 66 minutes. Molly finished ahead of Janet, with a faster time.
Let t represent the amount of time, in minutes, that it might have taken Molly to finish the race. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Let t represent the amount of time, in minutes, that it might have taken Molly to finish the race. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Answers
GPT-4o mini
To model the situation described, we can use the following inequality:
\[ t < 66 \]
This inequality indicates that the time \( t \) it took Molly to finish the race is less than the time it took Janet, which is 66 minutes.
### Graphing the Inequality
1. **X-Axis and Y-Axis**: The plot will have a horizontal axis representing the time in minutes (we can denote it as \( t \)).
2. **Plot the Point**: Plot the point at \( 66 \) on the number line.
3. **Open Circle**: Since the inequality is strict (Molly finished ahead of Janet), use an open circle at \( 66 \) to indicate that \( t \) cannot equal \( 66 \).
4. **Ray**: Draw a ray to the left of \( 66 \) to show that \( t \) can take on all values less than \( 66 \).
### Visual Representation
- **Open Circle at \( 66 \)**: \(\circ\)
- **Arrow Head Towards Left**: Indicates all values less than \( 66 \)
This graph visually represents the inequality \( t < 66 \).
Make sure that when you are graphing, the ray is clearly pointing to the left, indicating all possible times that are less than \( 66 \) minutes.
\[ t < 66 \]
This inequality indicates that the time \( t \) it took Molly to finish the race is less than the time it took Janet, which is 66 minutes.
### Graphing the Inequality
1. **X-Axis and Y-Axis**: The plot will have a horizontal axis representing the time in minutes (we can denote it as \( t \)).
2. **Plot the Point**: Plot the point at \( 66 \) on the number line.
3. **Open Circle**: Since the inequality is strict (Molly finished ahead of Janet), use an open circle at \( 66 \) to indicate that \( t \) cannot equal \( 66 \).
4. **Ray**: Draw a ray to the left of \( 66 \) to show that \( t \) can take on all values less than \( 66 \).
### Visual Representation
- **Open Circle at \( 66 \)**: \(\circ\)
- **Arrow Head Towards Left**: Indicates all values less than \( 66 \)
This graph visually represents the inequality \( t < 66 \).
Make sure that when you are graphing, the ray is clearly pointing to the left, indicating all possible times that are less than \( 66 \) minutes.