To determine the missing number of hours that corresponds to 24 miles in a proportional relationship, we can examine the distances passed per hour in the table.
We can first find the rate of miles per hour based on the given data points:
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For the time of 5 hours and 20 miles: \[ \text{Rate} = \frac{20 \text{ miles}}{5 \text{ hours}} = 4 \text{ miles per hour} \]
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For the time of 8 hours and 32 miles: \[ \text{Rate} = \frac{32 \text{ miles}}{8 \text{ hours}} = 4 \text{ miles per hour} \]
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For the time of 10 hours and 40 miles: \[ \text{Rate} = \frac{40 \text{ miles}}{10 \text{ hours}} = 4 \text{ miles per hour} \]
From these calculations, we can see that the rate is consistent at 4 miles per hour.
Now, we need to find the number of hours, \( h \), that corresponds to the distance of 24 miles. Since we know the rate is 4 miles per hour:
\[ \text{Distance} = \text{Rate} \times \text{Time} \] \[ 24 = 4 \times h \]
To find \( h \), we can rearrange the equation: \[ h = \frac{24}{4} = 6 \text{ hours} \]
Thus, the missing number is 6 hours.
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