Question

The table below shows the number of miles, m, Violet passed in h hours. What number is missing from the table?

It needs to show a proportional relationship!!!

Time in hours Distance passed
5 20
? 24
8 32
10 40
Group of answer choices

6

12

4

Answer 1

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:

1. For the time of 5 hours and 20 miles:
\[
\text{Rate} = \frac{20 \text{ miles}}{5 \text{ hours}} = 4 \text{ miles per hour}
\]

2. For the time of 8 hours and 32 miles:
\[
\text{Rate} = \frac{32 \text{ miles}}{8 \text{ hours}} = 4 \text{ miles per hour}
\]

3. 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.