Question Amelia is traveling from Los Angeles, California, to Mesa, Arizona. The total distance she will drive is 388 miles. Amelia would like to get to Mesa in approximately 7 hours. She is wondering at what speed she will have to travel in order to make that happen. Using the formula d=vt , rearrange the formula to highlight the quantity of interest.(1 point)

Answer 1

To find the speed at which Amelia needs to travel, we start with the formula for distance:

\[ d = vt \]

where:

• \( d \) is the distance,
• \( v \) is the speed,
• \( t \) is the time.

To highlight the quantity of interest (speed, \( v \)), we can rearrange the formula. We do this by solving for \( v \):

1. Divide both sides of the equation by \( t \):

\[ v = \frac{d}{t} \]

Now, we've isolated \( v \), which is the speed. This means Amelia can determine the speed she needs to travel by dividing the total distance by the time she wants to take to travel that distance.

In Amelia's case:

• \( d = 388 \) miles
• \( t = 7 \) hours

Using the rearranged formula, she can calculate her required speed:

\[ v = \frac{388 \text{ miles}}{7 \text{ hours}} \approx 55.43 \text{ miles per hour} \]

So, the highlighted quantity of interest (speed) is represented by the formula \( v = \frac{d}{t} \).