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 hour (60 minutes):
- Distance = 25 miles
- Pace = 25 miles / 60 minutes = \( \frac{25}{60} \) = 0.4167 miles per minute.
-
2 hours (120 minutes):
- Distance = 50 miles
- Pace = 50 miles / 120 minutes = \( \frac{50}{120} \) = 0.4167 miles per minute.
-
3 hours (180 minutes):
- Distance = 75 miles
- Pace = 75 miles / 180 minutes = \( \frac{75}{180} \) = 0.4167 miles per minute.
-
4 hours (240 minutes):
- Distance = 125 miles
- Pace = 125 miles / 240 minutes = \( \frac{125}{240} \) = approximately 0.5208 miles per minute.
-
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 \( \frac{1 \text{ hour}}{60 \text{ minutes}} \).
-
For \( x = 1 \):
- \( y = 27 \cdot 1 = 27 \) miles.
- Pace = 27 miles / 60 minutes = 0.45 miles per minute.
-
For \( x = 2 \):
- \( y = 27 \cdot 2 = 54 \) miles.
- Pace = 54 miles / 120 minutes = 0.45 miles per minute.
-
For \( x = 3 \):
- \( y = 27 \cdot 3 = 81 \) miles.
- Pace = 81 miles / 180 minutes = 0.45 miles per minute.
-
For \( x = 4 \):
- \( y = 27 \cdot 4 = 108 \) miles.
- Pace = 108 miles / 240 minutes = 0.45 miles per minute.
-
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.