Question

​Lucy's car has tires with a radius of 34 in. How many complete revolutions do her wheels make in 1​ mile? (Hint: First determine how many inches are in 1​ mile.) Use 3.14 for pi.
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Part 1
The exact number of revolutions is
  
enter your response here.
​(Type a whole number or a decimal rounded to the nearest hundredth as​ needed.)

Answer 1

To determine the number of complete revolutions Lucy's car tires make in 1 mile, we need to perform a few calculations.

1. **Convert miles to inches**:
- There are 5280 feet in a mile, and each foot has 12 inches:
\[
\text{Number of inches in 1 mile} = 5280 \, \text{feet} \times 12 \, \text{inches/foot} = 63360 \, \text{inches}
\]

2. **Calculate the circumference of the tire**:
- The circumference \( C \) of a circle (which is the distance traveled in one complete revolution of the tire) can be calculated using the formula:
\[
C = 2 \pi r
\]
where \( r \) is the radius of the tire (34 inches) and \( \pi \) is approximately 3.14.
\[
C = 2 \times 3.14 \times 34 \approx 215.44 \, \text{inches}
\]

3. **Determine the number of revolutions in 1 mile**:
- To find the number of complete revolutions, divide the total distance in inches (1 mile) by the circumference of one revolution:
\[
\text{Number of revolutions} = \frac{63360 \, \text{inches}}{215.44 \, \text{inches/revolution}} \approx 294.32
\]

Since the problem asks for the number of complete revolutions, we can take the whole number part of this result:
\[
\text{Complete revolutions} = 294
\]

Thus, the exact number of revolutions is approximately **294**.