Question
A track runner ran for 15 minutes, walked for 15 minutes, ran for another 20 minutes, and then stretched in place for 10 minutes.
Which graph describes the relationship between runner's total distance and time?
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 2.4, and a horizontal line segment from 0.8 comma 2.4 to 1 comma 2.4
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 0.1, and a horizontal line segment from 0.8 comma 0.1 to 1 comma 0.1
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a line segment from 0.8 comma 2.95 to 1 comma 3.15
Which graph describes the relationship between runner's total distance and time?
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 2.4, and a horizontal line segment from 0.8 comma 2.4 to 1 comma 2.4
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 0.1, and a horizontal line segment from 0.8 comma 0.1 to 1 comma 0.1
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a line segment from 0.8 comma 2.95 to 1 comma 3.15
Answers
GPT-4o mini
To determine which graph describes the relationship between the runner's total distance and time, we first need to analyze the runner's activity details:
1. **Running for 15 minutes:** Let's assume the runner has a pace of 5 miles per hour (which is a common running pace). In 15 minutes (which is 0.25 hours), the distance covered is:
\[
\text{Distance} = \text{Time} \times \text{Speed} = 0.25 \text{ hours} \times 5 \text{ miles/hour} = 1.25 \text{ miles}
\]
2. **Walking for 15 minutes:** A common walking pace is around 3 miles per hour. In 15 minutes (0.25 hours), the distance covered is:
\[
\text{Distance} = 0.25 \text{ hours} \times 3 \text{ miles/hour} = 0.75 \text{ miles}
\]
After the walking segment, the total distance is:
\[
1.25 \text{ miles} + 0.75 \text{ miles} = 2.00 \text{ miles}
\]
3. **Running for another 20 minutes:** Again, if we use the running pace of 5 miles per hour, for 20 minutes (which is about 0.33 hours):
\[
\text{Distance} = 0.33 \text{ hours} \times 5 \text{ miles/hour} \approx 1.67 \text{ miles}
\]
Adding this to the total distance:
\[
2.00 \text{ miles} + 1.67 \text{ miles} \approx 3.67 \text{ miles}
\]
4. **Stretching in place for 10 minutes:** Stretching does not add any distance, so our total distance remains:
\[
3.67 \text{ miles}
\]
Now, we can summarize the total distances at each segment of time:
- At 15 minutes (0.25 hours): **1.25 miles**
- At 30 minutes (0.50 hours): **2.00 miles**
- At 50 minutes (0.80 hours): **3.67 miles** (before stretching)
- At 60 minutes (1.00 hour): **3.67 miles** (after stretching)
Now, let's look back at the graphs provided:
1. The first graph shows:
- 0.25 hours = 1.25 miles
- 0.5 hours = 1.25 miles (horizontal line)
- 0.8 hours = 2.4 miles (incorrect)
- 1.0 hours = 2.4 miles (horizontal line)
(Thus not matching our values.)
2. The second graph shows:
- 0.25 hours = 1.25 miles
- 0.5 hours = 1.75 miles (incorrect)
- 0.8 hours = 2.95 miles (incorrect)
- 1.0 hours = 2.95 miles (horizontal line)
(Thus not matching our values.)
3. The third graph shows:
- 0.25 hours = 1.25 miles
- 0.5 hours = 1.25 miles (horizontal line, matching)
- 0.8 hours = 0.1 miles (incorrect)
- 1.0 hours = 0.1 miles (horizontal line)
(Thus not matching our values.)
4. The fourth graph shows:
- 0.25 hours = 1.25 miles
- 0.5 hours = 1.75 miles (incorrect)
- 0.8 hours = 2.95 miles (incorrect)
- 1.0 hours = 3.15 miles (incorrect)
(Thus not matching our values.)
Based on the analysis, none of the provided graphs accurately match the runner's total distances after each segment of time according to our calculations. If any of the speeds or assumptions varied, we might find a match, but as it stands, all graphs provided do not reflect the runner's total distance traveled based on the given information.
1. **Running for 15 minutes:** Let's assume the runner has a pace of 5 miles per hour (which is a common running pace). In 15 minutes (which is 0.25 hours), the distance covered is:
\[
\text{Distance} = \text{Time} \times \text{Speed} = 0.25 \text{ hours} \times 5 \text{ miles/hour} = 1.25 \text{ miles}
\]
2. **Walking for 15 minutes:** A common walking pace is around 3 miles per hour. In 15 minutes (0.25 hours), the distance covered is:
\[
\text{Distance} = 0.25 \text{ hours} \times 3 \text{ miles/hour} = 0.75 \text{ miles}
\]
After the walking segment, the total distance is:
\[
1.25 \text{ miles} + 0.75 \text{ miles} = 2.00 \text{ miles}
\]
3. **Running for another 20 minutes:** Again, if we use the running pace of 5 miles per hour, for 20 minutes (which is about 0.33 hours):
\[
\text{Distance} = 0.33 \text{ hours} \times 5 \text{ miles/hour} \approx 1.67 \text{ miles}
\]
Adding this to the total distance:
\[
2.00 \text{ miles} + 1.67 \text{ miles} \approx 3.67 \text{ miles}
\]
4. **Stretching in place for 10 minutes:** Stretching does not add any distance, so our total distance remains:
\[
3.67 \text{ miles}
\]
Now, we can summarize the total distances at each segment of time:
- At 15 minutes (0.25 hours): **1.25 miles**
- At 30 minutes (0.50 hours): **2.00 miles**
- At 50 minutes (0.80 hours): **3.67 miles** (before stretching)
- At 60 minutes (1.00 hour): **3.67 miles** (after stretching)
Now, let's look back at the graphs provided:
1. The first graph shows:
- 0.25 hours = 1.25 miles
- 0.5 hours = 1.25 miles (horizontal line)
- 0.8 hours = 2.4 miles (incorrect)
- 1.0 hours = 2.4 miles (horizontal line)
(Thus not matching our values.)
2. The second graph shows:
- 0.25 hours = 1.25 miles
- 0.5 hours = 1.75 miles (incorrect)
- 0.8 hours = 2.95 miles (incorrect)
- 1.0 hours = 2.95 miles (horizontal line)
(Thus not matching our values.)
3. The third graph shows:
- 0.25 hours = 1.25 miles
- 0.5 hours = 1.25 miles (horizontal line, matching)
- 0.8 hours = 0.1 miles (incorrect)
- 1.0 hours = 0.1 miles (horizontal line)
(Thus not matching our values.)
4. The fourth graph shows:
- 0.25 hours = 1.25 miles
- 0.5 hours = 1.75 miles (incorrect)
- 0.8 hours = 2.95 miles (incorrect)
- 1.0 hours = 3.15 miles (incorrect)
(Thus not matching our values.)
Based on the analysis, none of the provided graphs accurately match the runner's total distances after each segment of time according to our calculations. If any of the speeds or assumptions varied, we might find a match, but as it stands, all graphs provided do not reflect the runner's total distance traveled based on the given information.