## Step-by-Step Solution:
To solve this problem, we need to follow a series of steps that involve unit conversions, circumference calculations, and division. Let's go through each step in detail:
### Step 1: Convert the distance from meters to inches
The first step is to convert 3,000 meters into inches because the diameter of the bicycle wheel is given in inches.
1 meter = 39.3701 inches.
Therefore, to convert 3,000 meters to inches:
[tex]\[ \text{Distance in inches} = 3000 \times 39.3701 \][/tex]
### Step 2: Calculate the circumference of the wheel
The next step is to calculate the circumference of the bicycle wheel. The formula for the circumference [tex]\( C \)[/tex] of a circle is:
[tex]\[ C = \pi \times \text{Diameter} \][/tex]
Given:
- Diameter = 15 inches
- π (Pi) ≈ 3.14
Therefore, the circumference of the wheel is:
[tex]\[ \text{Circumference} = 3.14 \times 15 \][/tex]
### Step 3: Calculate the number of revolutions
Now we need to determine how many times the wheel will have to rotate entirely to cover the total distance. To find the number of revolutions, divide the total distance traveled in inches by the circumference of the wheel:
[tex]\[ \text{Number of revolutions} = \frac{\text{Total distance in inches}}{\text{Circumference in inches}} \][/tex]
### Step 4: Round to the nearest whole number
Finally, we round the resulting number of revolutions to the nearest whole number to get our final answer.
After performing all these steps, we find that the bicycle wheel will take approximately 2,508 revolutions to travel 3,000 meters when rounded to the nearest whole number.
Final Answer: Approximately 2,508 revolutions
