Question

The distance traveled by the blue car was monitored by a table.
number of hours, miles traveled
4, 216
5, 270
6, 324

Answer 1

To analyze the distance traveled by the blue car, we can derive the speed and create a model from the data you provided:

1. **Calculate the speed**: We can find the speed of the blue car for each hour from the distances shown.

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

For 4 hours:
\[
\text{Speed} = \frac{216 \text{ miles}}{4 \text{ hours}} = 54 \text{ miles per hour}
\]

For 5 hours:
\[
\text{Speed} = \frac{270 \text{ miles}}{5 \text{ hours}} = 54 \text{ miles per hour}
\]

For 6 hours:
\[
\text{Speed} = \frac{324 \text{ miles}}{6 \text{ hours}} = 54 \text{ miles per hour}
\]

From these calculations, we see that the blue car has a constant speed of 54 miles per hour.

2. **Create a general equation**: Knowing the speed is constant, we can write a linear equation for distance traveled over time:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

Substituting the constant speed we found:

\[
\text{Distance} = 54 \times \text{Time}
\]

3. **Check if the model fits the data**: We can use the hours from the table to see if our equation gives the correct distances:

- For \(t = 4\):
\[
\text{Distance} = 54 \times 4 = 216 \text{ miles}
\]
- For \(t = 5\):
\[
\text{Distance} = 54 \times 5 = 270 \text{ miles}
\]
- For \(t = 6\):
\[
\text{Distance} = 54 \times 6 = 324 \text{ miles}
\]

All calculated distances match those in the table, confirming the accuracy of our linear equation.

In summary, the blue car travels at a constant speed of 54 miles per hour, and the distance can be expressed by the equation:
\[
\text{Distance} = 54 \times \text{Time}
\]