To determine the slope (or constant speed) of each marathon runner from a graph or a table, you typically need data on distance and time.
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Calculate Constant Speed:
- The formula for speed is: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
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From the Graph:
- Look for two clear points on the graph for each runner. For example, if Fast Freddy runs 10 miles in 80 minutes and Speedy Sammy runs the same distance in 70 minutes:
- Fast Freddy: \[ \text{Speed} = \frac{10 \text{ miles}}{80 \text{ min}} = 0.125 \text{ mi/min} \]
- Speedy Sammy: \[ \text{Speed} = \frac{10 \text{ miles}}{70 \text{ min}} \approx 0.143 \text{ mi/min} \]
- Look for two clear points on the graph for each runner. For example, if Fast Freddy runs 10 miles in 80 minutes and Speedy Sammy runs the same distance in 70 minutes:
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From the Table:
- If data is given in a table format showing distance and time at various intervals for each runner, you can do similar calculations:
- Identify the total distance and the total time for each runner, and apply the same speed formula.
- If data is given in a table format showing distance and time at various intervals for each runner, you can do similar calculations:
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Comparison:
- Once you have the speeds:
- If Fast Freddy = 0.125 mi/min and Speedy Sammy = 0.143 mi/min, then Speedy Sammy ran faster.
- Once you have the speeds:
If you provide specific data points or information from the graph and table, I can help calculate the exact speeds of Fast Freddy and Speedy Sammy, and clearly identify who ran faster.