The graph shows the distances traveled by two runners over several hours.

Question

Which runner is moving at a faster rate?



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is moving at a faster rate.



Graph in the coordinate plane with title distance versus time. Vertical axis is labeled distance in miles. Horizontal axis is labeled time in hours. A ray labeled runner A starts at point begin ordered pair 0 comma 0 end ordered pair and goes through point begin ordered pair 8 comma 5 end ordered pair. A ray labeled runner B starts at point begin ordered pair 0 comma 0 end ordered pair and goes through point begin ordered pair 10 comma 2 end ordered pair.

Answer 1

To determine which runner is moving at a faster rate, we can look at the slopes of the lines that represent their distances traveled over time on the graph.

1. Runner A starts at (0, 0) and goes through (8, 5). The slope (rate of distance per time) can be calculated as: \[ \text{slope of Runner A} = \frac{\Delta y}{\Delta x} = \frac{5 - 0}{8 - 0} = \frac{5}{8} \text{ miles per hour.} \]

2. Runner B starts at (0, 0) and goes through (10, 2). The slope can be calculated as: \[ \text{slope of Runner B} = \frac{\Delta y}{\Delta x} = \frac{2 - 0}{10 - 0} = \frac{2}{10} = \frac{1}{5} \text{ miles per hour.} \]

Now, we can compare the slopes:

• Runner A: \( \frac{5}{8} \) miles per hour
• Runner B: \( \frac{1}{5} \) miles per hour

To compare these values, we can convert them to decimals:

• \( \frac{5}{8} = 0.625 \) miles per hour
• \( \frac{1}{5} = 0.2 \) miles per hour

Since \( 0.625 > 0.2 \), we can conclude:

Runner A is moving at a faster rate.

So, the completed statement is:

Runner A is moving at a faster rate.