Question
Christy went jogging on Saturday. The table shows how far she had jogged after various times.
Distance (miles) 4.5 7.5 10.5
Time (hours)
0.75 1.25 1.75
Part A
Does it appear that Christy ran the same pace from when she began until she reached 7.5 miles?
Explain why or why not.
Enter your explanation in the box provided.
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Assessment 2
53
GO ON
Part B
Does it appear that the relationship between the distances Christy ran and the amount of time it took
is a proportional relationship? Explain.
Enter your answer and explanation in the box provided.
Part C
What do you think Christy’s distance was after 1 hour? Explain.
Enter your answer and explanation in the box provided.
Distance (miles) 4.5 7.5 10.5
Time (hours)
0.75 1.25 1.75
Part A
Does it appear that Christy ran the same pace from when she began until she reached 7.5 miles?
Explain why or why not.
Enter your explanation in the box provided.
Downloaded by S. FARSAKH at SOUTHEAST MIDDLE SCHOOL. This resource expires on 6/30/2025.
©Curriculum Associates, LLC Copying is not permitted.
Assessment 2
53
GO ON
Part B
Does it appear that the relationship between the distances Christy ran and the amount of time it took
is a proportional relationship? Explain.
Enter your answer and explanation in the box provided.
Part C
What do you think Christy’s distance was after 1 hour? Explain.
Enter your answer and explanation in the box provided.
Answers
Answered by
GPT-4o mini
To answer your questions, let's analyze the provided data and calculate Christy's pace at different intervals.
### Part A:
To determine if Christy ran at the same pace from 0 to 7.5 miles, we can calculate her pace during that interval.
- From 0 to 4.5 miles, it took her 0.75 hours:
\[
\text{Pace} = \frac{\text{Distance}}{\text{Time}} = \frac{4.5 \text{ miles}}{0.75 \text{ hours}} = 6 \text{ miles per hour}
\]
- From 4.5 miles to 7.5 miles (which is an additional 3 miles), it took her an additional:
\( 1.25 - 0.75 = 0.5 \) hours:
\[
\text{Pace} = \frac{3 \text{ miles}}{0.5 \text{ hours}} = 6 \text{ miles per hour}
\]
Since both intervals yielded the same pace of 6 miles per hour, it appears that Christy did maintain the same pace from the start until she reached 7.5 miles.
### Part B:
To determine if the relationship between the distances and the times is proportional, we need to check if the ratio of distance to time is constant.
- From 0 to 4.5 miles:
\[
\frac{4.5 \text{ miles}}{0.75 \text{ hours}} = 6
\]
- From 0 to 7.5 miles:
\[
\frac{7.5 \text{ miles}}{1.25 \text{ hours}} = 6
\]
- From 0 to 10.5 miles:
\[
\frac{10.5 \text{ miles}}{1.75 \text{ hours}} = 6
\]
Since the ratio is consistently 6 miles per hour across all intervals, this indicates a proportional relationship between the distance Christy ran and the time it took.
### Part C:
To estimate Christy's distance after 1 hour, we can use her constant pace of 6 miles per hour.
At a pace of 6 miles per hour for 1 hour, Christy would run:
\[
\text{Distance} = \text{Pace} \times \text{Time} = 6 \text{ miles/hour} \times 1 \text{ hour} = 6 \text{ miles}
\]
Thus, after 1 hour, it is reasonable to conclude that Christy jogged 6 miles.
In summary:
- **Part A:** Christy maintained the same pace during the first segment to 7.5 miles.
- **Part B:** The relationship is proportional, as the pace is consistent at 6 miles per hour.
- **Part C:** After 1 hour, Christy jogged approximately 6 miles.
### Part A:
To determine if Christy ran at the same pace from 0 to 7.5 miles, we can calculate her pace during that interval.
- From 0 to 4.5 miles, it took her 0.75 hours:
\[
\text{Pace} = \frac{\text{Distance}}{\text{Time}} = \frac{4.5 \text{ miles}}{0.75 \text{ hours}} = 6 \text{ miles per hour}
\]
- From 4.5 miles to 7.5 miles (which is an additional 3 miles), it took her an additional:
\( 1.25 - 0.75 = 0.5 \) hours:
\[
\text{Pace} = \frac{3 \text{ miles}}{0.5 \text{ hours}} = 6 \text{ miles per hour}
\]
Since both intervals yielded the same pace of 6 miles per hour, it appears that Christy did maintain the same pace from the start until she reached 7.5 miles.
### Part B:
To determine if the relationship between the distances and the times is proportional, we need to check if the ratio of distance to time is constant.
- From 0 to 4.5 miles:
\[
\frac{4.5 \text{ miles}}{0.75 \text{ hours}} = 6
\]
- From 0 to 7.5 miles:
\[
\frac{7.5 \text{ miles}}{1.25 \text{ hours}} = 6
\]
- From 0 to 10.5 miles:
\[
\frac{10.5 \text{ miles}}{1.75 \text{ hours}} = 6
\]
Since the ratio is consistently 6 miles per hour across all intervals, this indicates a proportional relationship between the distance Christy ran and the time it took.
### Part C:
To estimate Christy's distance after 1 hour, we can use her constant pace of 6 miles per hour.
At a pace of 6 miles per hour for 1 hour, Christy would run:
\[
\text{Distance} = \text{Pace} \times \text{Time} = 6 \text{ miles/hour} \times 1 \text{ hour} = 6 \text{ miles}
\]
Thus, after 1 hour, it is reasonable to conclude that Christy jogged 6 miles.
In summary:
- **Part A:** Christy maintained the same pace during the first segment to 7.5 miles.
- **Part B:** The relationship is proportional, as the pace is consistent at 6 miles per hour.
- **Part C:** After 1 hour, Christy jogged approximately 6 miles.