The problem states that Charles runs 100 meters in 13 seconds at a constant speed. We need to identify which of the given graphs correctly represents Charles' speed.

1. Problem Description

The problem states that Charles runs 100 meters in 13 seconds at a constant speed. We need to identify which of the given graphs correctly represents Charles' speed.

2. Solution Steps

We are given that Charles runs 100 meters in 13 seconds. A graph representing this should show a linear relationship between distance and time, where the point (13, 100) lies on the line, assuming the line starts at (0,0).

Graph W shows the distance reaching 100 meters at 100 seconds, which is not correct.

Graph X shows the distance reaching approximately 80 meters at 10 seconds, then proportionally, it would run more than 100 meters in 13 seconds. We need to estimate where the graph would be at 13 seconds. Looking at the graph, the distance at 13 seconds is approximately 100m. The point (13, 100) would lie on this line.

To be absolutely certain, we could compare the rate of change (slope) of the line in graph X to the calculated rate of change.

Charles runs 100 meters in 13 seconds, his speed is:

$speed = \frac{distance}{time}$

$speed = \frac{100}{13} \approx 7.69 m/s$

This means, the distance (in meters) is approximately equal to $7.69$ times the time (in seconds):

$distance \approx 7.69 \times time$

Let's check point (10,80) on graph X:

$80 = 7.69 \times 10.4$ (Approximately, considering the uncertainty when taking a point from the graph.)

Because point (13, 100) will more or less satisfy the condition, graph X correctly represents the speed.

3. Final Answer

X.