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
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
Answers
GPT-4o mini
To determine which graph describes the runner's total distance over time, we first need to calculate the total distance covered during each segment of the activity.
1. **Running for 15 minutes**: Let's assume the runner runs at an average pace of 5 miles per hour (this is a typical pace).
- Distance = Speed × Time = 5 mph × (15/60) hours = 5 × 0.25 = 1.25 miles.
2. **Walking for 15 minutes**: Assume the walker walks at an average pace of 3 miles per hour.
- Distance = Speed × Time = 3 mph × (15/60) hours = 3 × 0.25 = 0.75 miles.
3. **Running for another 20 minutes**: Continuing with the same running speed of 5 miles per hour.
- Distance = 5 mph × (20/60) hours = 5 × (1/3) = 5/3 = approximately 1.67 miles.
4. **Stretching in place for 10 minutes**: During stretching, the distance covered is 0 miles.
Now, let's add the segments to find the total distance:
- **First Run**: 1.25 miles
- **Walking**: 0.75 miles
- **Second Run**: 1.67 miles
- **Stretching**: 0 miles
Total distance = 1.25 + 0.75 + 1.67 = 3.67 miles.
Now let's segment the total time:
- Total time = 15 minutes + 15 minutes + 20 minutes + 10 minutes = 60 minutes = 1 hour.
Putting this together:
- From 0 to 15 minutes (0 to 0.25 hours), the runner covers 1.25 miles (increases linearly).
- From 0.25 hours (15 minutes) to 0.5 hours (30 minutes), the distance remains constant at 1.25 miles (horizontal line).
- From 0.5 hours (30 minutes) to 0.8 hours (48 minutes), the distance increases from 1.25 miles to 2.4 miles (increases linearly during the second run).
- From 0.8 hours (48 minutes) to 1 hour, the distance remains constant at 2.4 miles (horizontal line as the runner is stretching).
Now, matching this to the options:
- The first graph has the following characteristics: It starts with a segment that goes from (0,0) to (0.25,1.25), then a horizontal line from (0.25,1.25) to (0.5, 1.25), followed by a segment that goes from (0.5, 1.25) to (0.8, 2.4), and then a horizontal line from (0.8, 2.4) to (1, 2.4).
This description fits the calculated distances and time perfectly, so **the first graph** is the correct representation of the relationship between the runner's total distance and time.
1. **Running for 15 minutes**: Let's assume the runner runs at an average pace of 5 miles per hour (this is a typical pace).
- Distance = Speed × Time = 5 mph × (15/60) hours = 5 × 0.25 = 1.25 miles.
2. **Walking for 15 minutes**: Assume the walker walks at an average pace of 3 miles per hour.
- Distance = Speed × Time = 3 mph × (15/60) hours = 3 × 0.25 = 0.75 miles.
3. **Running for another 20 minutes**: Continuing with the same running speed of 5 miles per hour.
- Distance = 5 mph × (20/60) hours = 5 × (1/3) = 5/3 = approximately 1.67 miles.
4. **Stretching in place for 10 minutes**: During stretching, the distance covered is 0 miles.
Now, let's add the segments to find the total distance:
- **First Run**: 1.25 miles
- **Walking**: 0.75 miles
- **Second Run**: 1.67 miles
- **Stretching**: 0 miles
Total distance = 1.25 + 0.75 + 1.67 = 3.67 miles.
Now let's segment the total time:
- Total time = 15 minutes + 15 minutes + 20 minutes + 10 minutes = 60 minutes = 1 hour.
Putting this together:
- From 0 to 15 minutes (0 to 0.25 hours), the runner covers 1.25 miles (increases linearly).
- From 0.25 hours (15 minutes) to 0.5 hours (30 minutes), the distance remains constant at 1.25 miles (horizontal line).
- From 0.5 hours (30 minutes) to 0.8 hours (48 minutes), the distance increases from 1.25 miles to 2.4 miles (increases linearly during the second run).
- From 0.8 hours (48 minutes) to 1 hour, the distance remains constant at 2.4 miles (horizontal line as the runner is stretching).
Now, matching this to the options:
- The first graph has the following characteristics: It starts with a segment that goes from (0,0) to (0.25,1.25), then a horizontal line from (0.25,1.25) to (0.5, 1.25), followed by a segment that goes from (0.5, 1.25) to (0.8, 2.4), and then a horizontal line from (0.8, 2.4) to (1, 2.4).
This description fits the calculated distances and time perfectly, so **the first graph** is the correct representation of the relationship between the runner's total distance and time.