Question

A car is traveling down the road at a constant speed. Every 3 hours, the car travels 150 miles. Write an equation that describes the proportional relationship between the distance d
in miles and the time t
in hours.

Is option 1, option 2, or option 3 the correct equation?

Option 1: d=50t

Option 2: t=50d

Option 3: d−t=50


(1 point)
Option

Answer 1

To find the relationship between distance \( d \) (in miles) and time \( t \) (in hours), we start with the information given:

The car travels 150 miles in 3 hours.

To find the speed of the car, we calculate:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ miles per hour}
\]

This means the car travels 50 miles for each hour. Therefore, the distance \( d \) can be represented as:

\[
d = 50t
\]

This relationship shows that distance is proportional to time, with a constant of proportionality equal to 50.

Now let's evaluate the options provided:

- **Option 1: \( d = 50t \)** - This correctly describes the relationship between distance and time.
- **Option 2: \( t = 50d \)** - This is not correct; it incorrectly relates time to distance.
- **Option 3: \( d - t = 50 \)** - This also does not represent the correct relationship.

Therefore, the correct equation is:

**Option 1: \( d = 50t \)**.