To find how fast the car is traveling, we need to consider the information given:

• The radius of the tires = 13 inches
• The tires are revolving at a rate of 744 revolutions per minute (rpm)

Step 1: Calculate the circumference of the tire.

The circumference of a circle is given by the formula:

$C = 2\pi r$

where $r$ is the radius. Since the radius is 13 inches:

$C = 2\pi(13) = 26\pi \, \text{inches}$

Step 2: Determine how far the car travels in one minute.

The car travels a distance equal to the circumference of the tire for each revolution. If the tire is revolving 744 times per minute, the total distance traveled in one minute is:

$\text{Distance per minute} = 744 \times 26\pi = 19344\pi \, \text{inches}$

Step 3: Convert the distance from inches per minute to miles per hour (mph).

There are 60 minutes in an hour and 63,360 inches in a mile. To convert inches per minute to miles per hour, we use the following conversion factor:

$\frac{1 \, \text{mile}}{63,360 \, \text{inches}} \times \frac{60 \, \text{minutes}}{1 \, \text{hour}}$

So, the car's speed in miles per hour (mph) is:

$\text{Speed} = \frac{19344\pi \times 60}{63,360}$

Simplifying:

$\text{Speed} = \frac{1160640\pi}{63360} = \frac{403\pi}{220} \, \text{mph}$

Step 4: Conclusion

The car is traveling at a speed of:

$\boxed{\frac{403\pi}{220}} \, \text{mph}$

This matches option A.

Would you like further details or have any questions? Here are 5 related questions:

1. How would the speed change if the radius of the tire was doubled?
2. If the car's speed is given in miles per minute, how would you convert it to miles per hour?
3. How does tire size affect the speed of a vehicle?
4. What is the relationship between tire revolutions and the distance traveled?
5. How can we estimate the time it takes for the car to travel 1 mile?

Tip: To ensure accuracy in converting between different units, always use consistent conversion factors for distance and time (e.g., inches to miles, minutes to hours).