Question
Will and luke both bikers.
Will's pace is shown in the table below.
Luke's pace is shown with the equation y = 27x
Time ( hours)
1,2,3,4,5,10
Distance (miles)
25,50,75,125,250
What is will's miles per minute pace?
What is luke's miles per minute pace?
Will's per minutes is
Luke's miles per minute is
Will's pace is shown in the table below.
Luke's pace is shown with the equation y = 27x
Time ( hours)
1,2,3,4,5,10
Distance (miles)
25,50,75,125,250
What is will's miles per minute pace?
What is luke's miles per minute pace?
Will's per minutes is
Luke's miles per minute is
Answers
Answered by
GPT-4o mini
To find Will's miles per minute pace, we will calculate his pace based on the distance he travels in a given time.
From the table:
- Will's distances at corresponding times are as follows:
- At 1 hour: 25 miles
- At 2 hours: 50 miles
- At 3 hours: 75 miles
- At 4 hours: 125 miles
- At 5 hours: 250 miles
- At 10 hours: The distance is not given explicitly in the table beyond mileages for 5 hours.
Let's derive Will's pace in miles per minute for the available data:
1. **1 hour (60 minutes)**:
- Distance = 25 miles
- Pace = 25 miles / 60 minutes = \( \frac{25}{60} \) = 0.4167 miles per minute.
2. **2 hours (120 minutes)**:
- Distance = 50 miles
- Pace = 50 miles / 120 minutes = \( \frac{50}{120} \) = 0.4167 miles per minute.
3. **3 hours (180 minutes)**:
- Distance = 75 miles
- Pace = 75 miles / 180 minutes = \( \frac{75}{180} \) = 0.4167 miles per minute.
4. **4 hours (240 minutes)**:
- Distance = 125 miles
- Pace = 125 miles / 240 minutes = \( \frac{125}{240} \) = approximately 0.5208 miles per minute.
5. **5 hours (300 minutes)**:
- Distance = 250 miles
- Pace = 250 miles / 300 minutes = \( \frac{250}{300} \) = \( \frac{5}{6} \) = approximately 0.8333 miles per minute.
From this, Will's miles per minute pace varies based on distance traveled over time. However, from the best consistent average on the data available between 1 to 3 hours, we can state a more consistent pace of approximately **0.4167 miles/minute**.
Next, let's calculate Luke's pace from the equation given: \( y = 27x \).
Where \( y \) is the distance in miles and \( x \) is the time in hours.
To convert to minutes, we need to multiply by the conversion factor \( \frac{1 \text{ hour}}{60 \text{ minutes}} \).
1. For \( x = 1 \):
- \( y = 27 \cdot 1 = 27 \) miles.
- Pace = 27 miles / 60 minutes = 0.45 miles per minute.
2. For \( x = 2 \):
- \( y = 27 \cdot 2 = 54 \) miles.
- Pace = 54 miles / 120 minutes = 0.45 miles per minute.
3. For \( x = 3 \):
- \( y = 27 \cdot 3 = 81 \) miles.
- Pace = 81 miles / 180 minutes = 0.45 miles per minute.
4. For \( x = 4 \):
- \( y = 27 \cdot 4 = 108 \) miles.
- Pace = 108 miles / 240 minutes = 0.45 miles per minute.
5. For \( x = 5 \):
- \( y = 27 \cdot 5 = 135 \) miles.
- Pace = 135 miles / 300 minutes = 0.45 miles per minute.
From all of this, we find that Luke consistently has a pace of **0.45 miles/minute**.
**Summary:**
- Will’s miles per minute pace is approximately **0.4167 miles/minute**.
- Luke’s miles per minute pace is **0.45 miles/minute**.
From the table:
- Will's distances at corresponding times are as follows:
- At 1 hour: 25 miles
- At 2 hours: 50 miles
- At 3 hours: 75 miles
- At 4 hours: 125 miles
- At 5 hours: 250 miles
- At 10 hours: The distance is not given explicitly in the table beyond mileages for 5 hours.
Let's derive Will's pace in miles per minute for the available data:
1. **1 hour (60 minutes)**:
- Distance = 25 miles
- Pace = 25 miles / 60 minutes = \( \frac{25}{60} \) = 0.4167 miles per minute.
2. **2 hours (120 minutes)**:
- Distance = 50 miles
- Pace = 50 miles / 120 minutes = \( \frac{50}{120} \) = 0.4167 miles per minute.
3. **3 hours (180 minutes)**:
- Distance = 75 miles
- Pace = 75 miles / 180 minutes = \( \frac{75}{180} \) = 0.4167 miles per minute.
4. **4 hours (240 minutes)**:
- Distance = 125 miles
- Pace = 125 miles / 240 minutes = \( \frac{125}{240} \) = approximately 0.5208 miles per minute.
5. **5 hours (300 minutes)**:
- Distance = 250 miles
- Pace = 250 miles / 300 minutes = \( \frac{250}{300} \) = \( \frac{5}{6} \) = approximately 0.8333 miles per minute.
From this, Will's miles per minute pace varies based on distance traveled over time. However, from the best consistent average on the data available between 1 to 3 hours, we can state a more consistent pace of approximately **0.4167 miles/minute**.
Next, let's calculate Luke's pace from the equation given: \( y = 27x \).
Where \( y \) is the distance in miles and \( x \) is the time in hours.
To convert to minutes, we need to multiply by the conversion factor \( \frac{1 \text{ hour}}{60 \text{ minutes}} \).
1. For \( x = 1 \):
- \( y = 27 \cdot 1 = 27 \) miles.
- Pace = 27 miles / 60 minutes = 0.45 miles per minute.
2. For \( x = 2 \):
- \( y = 27 \cdot 2 = 54 \) miles.
- Pace = 54 miles / 120 minutes = 0.45 miles per minute.
3. For \( x = 3 \):
- \( y = 27 \cdot 3 = 81 \) miles.
- Pace = 81 miles / 180 minutes = 0.45 miles per minute.
4. For \( x = 4 \):
- \( y = 27 \cdot 4 = 108 \) miles.
- Pace = 108 miles / 240 minutes = 0.45 miles per minute.
5. For \( x = 5 \):
- \( y = 27 \cdot 5 = 135 \) miles.
- Pace = 135 miles / 300 minutes = 0.45 miles per minute.
From all of this, we find that Luke consistently has a pace of **0.45 miles/minute**.
**Summary:**
- Will’s miles per minute pace is approximately **0.4167 miles/minute**.
- Luke’s miles per minute pace is **0.45 miles/minute**.