Question

a car travels 6,160 feet per minute. If the radius of each tire on the car is two feet how many revolutions does one of these tires make in a single minute?

Answer 1

To find out how many revolutions the tire makes in a minute, we first need to calculate the circumference of the tire. The formula for the circumference \( C \) of a circle is given by:

\[
C = 2 \pi r
\]

where \( r \) is the radius. Here, the radius of the tire is 2 feet.

Calculating the circumference:

\[
C = 2 \pi (2) = 4 \pi \text{ feet}
\]

Next, we need to find out how many times the tire rotates in one minute. We do this by dividing the distance traveled by the circumference of the tire:

\[
\text{Revolutions per minute} = \frac{\text{Distance traveled in a minute}}{\text{Circumference of the tire}}
\]

The car travels 6,160 feet per minute, so we plug in our values:

\[
\text{Revolutions per minute} = \frac{6,160 \text{ feet}}{4 \pi \text{ feet}}
\]

Calculating this gives:

\[
\text{Revolutions per minute} = \frac{6,160}{4 \pi} \approx \frac{6,160}{12.5664} \approx 490.87
\]

Rounding down, we find that the tire makes approximately 491 revolutions per minute.

Thus, the answer is:

**The tire makes approximately 491 revolutions per minute.**