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Answer :
Sure, let's tackle this problem step-by-step.
### Part (a): Fill out the Table
First, we'll fill out a table that shows the distance each runner has traveled from the start line at different times:
Given Data:
- Zeke runs 2 yards every second.
- Niko starts 12 yards ahead and runs 1 yard every 2 seconds, which is the same as 0.5 yards every second.
Table:
| Time (x seconds) | Zeke's Distance (yds) | Niko's Distance (yds) |
|------------------|-----------------------|-----------------------|
| 0 | 0 | 12 |
| 5 | 10 | 14.5 |
| 10 | 20 | 17 |
| 15 | 30 | 19.5 |
| 20 | 40 | 22 |
### Part (b): Write Equations for Distances
Next, we need to write equations that describe the distance of each runner from the start line as a function of time [tex]\(x\)[/tex].
1. Zeke's Distance:
- Zeke runs continuously at a speed of 2 yards per second.
- So the distance [tex]\(y\)[/tex] that Zeke travels after [tex]\(x\)[/tex] seconds can be modeled by the equation:
[tex]\[
\text{Zeke's Distance: } y = 2x
\][/tex]
2. Niko's Distance:
- Niko starts with a 12-yard head start and covers 0.5 yards every second.
- Therefore, the distance [tex]\(y\)[/tex] that Niko travels after [tex]\(x\)[/tex] seconds can be described by:
[tex]\[
\text{Niko's Distance: } y = 0.5x + 12
\][/tex]
These equations give you the distance each runner has covered over time from the start line.
### Part (a): Fill out the Table
First, we'll fill out a table that shows the distance each runner has traveled from the start line at different times:
Given Data:
- Zeke runs 2 yards every second.
- Niko starts 12 yards ahead and runs 1 yard every 2 seconds, which is the same as 0.5 yards every second.
Table:
| Time (x seconds) | Zeke's Distance (yds) | Niko's Distance (yds) |
|------------------|-----------------------|-----------------------|
| 0 | 0 | 12 |
| 5 | 10 | 14.5 |
| 10 | 20 | 17 |
| 15 | 30 | 19.5 |
| 20 | 40 | 22 |
### Part (b): Write Equations for Distances
Next, we need to write equations that describe the distance of each runner from the start line as a function of time [tex]\(x\)[/tex].
1. Zeke's Distance:
- Zeke runs continuously at a speed of 2 yards per second.
- So the distance [tex]\(y\)[/tex] that Zeke travels after [tex]\(x\)[/tex] seconds can be modeled by the equation:
[tex]\[
\text{Zeke's Distance: } y = 2x
\][/tex]
2. Niko's Distance:
- Niko starts with a 12-yard head start and covers 0.5 yards every second.
- Therefore, the distance [tex]\(y\)[/tex] that Niko travels after [tex]\(x\)[/tex] seconds can be described by:
[tex]\[
\text{Niko's Distance: } y = 0.5x + 12
\][/tex]
These equations give you the distance each runner has covered over time from the start line.
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