Question

use the image to answer the question.
the graph represents 4 runners running toward the finish line. interpret the graph to determine which runner finishes the race in second place.
(1 point)
○ runner d
○ runner c
○ runner b
○ runner a

Explanation:

Step1: Analyze Runner A's Finish Time

Runner A's line reaches \( y = 10 \) (finish line) around \( x \approx 2 \) seconds (visually, the red line hits 10m near \( x = 2 \)).

Step2: Analyze Runner B's Finish Time

Runner B's dashed line (black) reaches 10m around \( x \approx 3 \) seconds (since at \( x = 2 \), it's below 10m, and by \( x = 3 \), it's near or at 10m? Wait, no—wait, the finish line is 10m. Let's check when each runner's distance is 10m. Runner A: ~2s, Runner B: let's see the dashed black line. At \( x = 2 \), it's at some height, but when does it reach 10m? Wait, Runner C (blue dashed) and Runner D (dashed gray). Wait, re - examine: Runner A (red) starts at (0,0), goes up steeply. Runner B (black dashed) starts at (0,0)? No, wait the graph: Runner A (red) from (0,0), Runner B (black dashed) – wait, the y - axis for Runner D starts at (0,5)? No, no: the y - axis is distance (meters), x - axis time (seconds). Runner A: (0,0) to (2,10) maybe? Runner B: let's see the black dashed line. Wait, the finish line is \( y = 10 \). So we need to find for each runner, the \( x \) - value when \( y = 10 \).

Runner A: \( y = 10 \) at \( x \approx 2 \) (first to finish).

Runner B: Let's see the black dashed line. When does it reach \( y = 10 \)? Looking at the graph, Runner B's line (black dashed) – wait, maybe I mislabeled. Wait, the graph has Runner A (red), Runner B (black dashed), Runner C (blue dashed), Runner D (gray dashed).

Wait, Runner A: from (0,0) to (2,10) (so time ~2s to finish).

Runner B: when does its line reach \( y = 10 \)? Let's see the x - axis. At \( x = 3 \), where is Runner B? Wait, maybe I made a mistake. Let's check Runner C (blue dashed): starts at (0,1)? No, Runner D starts at (0,5). Wait, no: the y - intercept for Runner D is 5 (at \( x = 0 \), \( y = 5 \)). Runner A: (0,0), Runner B: (0,0)? No, the labels: Runner A (blue text), Runner B (blue text), etc.

Wait, correct approach: For each runner, find the \( x \) (time) when \( y = 10 \) (distance = 10m).

Runner A: \( y = 10 \) at \( x \approx 2 \) (first).

Runner B: Let's look at the black dashed line (Runner B). When does its distance reach 10m? Let's see the slope. Runner A: slope \( \frac{10 - 0}{2 - 0}=5 \) m/s. Runner B: let's see, at \( x = 2 \), where is Runner B? The black dashed line at \( x = 2 \) is at some height, but when does it reach 10m? Wait, maybe Runner B's line reaches 10m at \( x \approx 3 \) seconds? No, wait Runner C (blue dashed) – let's see Runner C: from (0,1) (no, at \( x = 0 \), Runner D is at \( y = 5 \), Runner A at (0,0), Runner B at (0,0)? No, I think I messed up the initial points.

Wait, the key is: the runner who finishes second has the second - smallest time to reach \( y = 10 \).

Runner A: ~2s (first).

Runner B: Let's check the black dashed line. If Runner A is ~2s, then Runner B: when does its line hit 10m? Let's see the x - axis. The black dashed line (Runner B) – at \( x = 2 \), it's below 10m, at \( x = 3 \), is it at 10m? Wait, maybe Runner B's finish time is around 3s? No, wait Runner C (blue dashed) – let's see Runner C: from (0,1) (no, at \( x = 0 \), Runner C is at \( y = 1 \)? No, the y - axis is distance, so at \( x = 0 \), Runner D is at \( y = 5 \), Runner A at \( y = 0 \), Runner B at \( y = 0 \), Runner C at \( y = 1 \)? No, this is confusing. Wait, the correct way: the finish line is \( y = 10 \). So we find the \( x \) (time) for each runner when \( y = 10 \).

Runner A: \( x \approx 2 \) (first).

Runner B: Let's look at the black dashed line. When \( y = 10 \), what's \( x \)? If we follow the black dashed line, it reaches \( y = 10 \) at \( x \approx 3 \) (second to finish).

Runner C: blue dashed line – when does it reach \( y = 10 \)? At \( x \approx 4 \) or 5?

Runner D: gray dashed line – starts at \( y = 5 \) at \( x = 0 \), so it will take longer, since it has to go from 5m to 10m, so its time to finish is much longer.

So the order of finishing (from least time to most): Runner A (≈2s), Runner B (≈3s), Runner C (≈4 - 5s), Runner D (much longer). So the second - place finisher is Runner B? Wait, no—wait, maybe I messed up Runner B and Runner C. Wait, no, let's re - examine the graph again. Wait, the black dashed line (Runner B) – maybe I had the runners wrong. Wait, the problem is to find which runner finishes second. So first, Runner A finishes first (earliest time to 10m). Then Runner B? Wait, no, maybe Runner B is not. Wait, maybe Runner B is the black dashed line, but when we look at the graph, Runner A (red) finishes at ~2s, Runner B (black dashed) finishes at ~3s, Runner C (blue dashed) finishes at ~4s, Runner D later. So the second - place finisher is Runner B? Wait, but the options are Runner D, Runner C, Runner B, Runner A. Wait, no, the options are: Runner D, Runner C, Runner B, Runner A. Wait, maybe my initial analysis is wrong. Wait, let's check the graph again.

Wait, Runner A: red line, from (0,0) to (2,10) (time 2s).

Runner B: black dashed line – let's see, at \( x = 2 \), it's at some distance, but when does it reach 10m? Wait, maybe Runner B is not starting at (0,0). Wait, the y - intercept for Runner D is 5, so Runner D starts at (0,5), so its distance at \( x = 0 \) is 5m. Runner A: (0,0), Runner B: (0,0), Runner C: (0,1)? No, this is a misinterpretation. The correct way is: the graph is a distance - time graph, where each line represents a runner's distance over time. The finish line is at \( y = 10 \) meters. So we need to find for each runner, the time (x - value) when their distance (y - value) is 10 meters.

- Runner A: The red line reaches \( y = 10 \) at \( x \approx 2 \) seconds (first to finish).
- Runner B: The black dashed line – let's follow it. When does it reach \( y = 10 \)? Looking at the graph, it reaches \( y = 10 \) at \( x \approx 3 \) seconds (second to finish).
- Runner C: The blue dashed line – reaches \( y = 10 \) at \( x \approx 4 \) or 5 seconds (third or later).
- Runner D: The gray dashed line – starts at \( y = 5 \) at \( x = 0 \), so it will take much longer to reach \( y = 10 \) (since it has to cover 5 more meters, and its slope is shallow).

So the runner who finishes second is Runner B.

Answer:

Runner B