A racetrack is in the form of a ring whose inner circumference is 264 m and the outer circumference is 308 m. Find the width of the track.

Answer

To find the width of the racetrack, we need to follow these steps:

### Step 1: Understand the relationship between circumference and radius.
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 2: Find the radius of the inner circle.
We know the inner circumference is 264 m. Using the formula for circumference:
\[ 264 = 2\pi r_1 \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ 264 = 2 \times \frac{22}{7} \times r_1 \]
Now, simplify the equation to find \( r_1 \):
\[ 264 = \frac{44}{7} r_1 \]
Multiplying both sides by 7 to eliminate the fraction:
\[ 264 \times 7 = 44 r_1 \]
\[ 1848 = 44 r_1 \]
Now, divide both sides by 44:
\[ r_1 = \frac{1848}{44} = 42 \text{ m} \]

### Step 3: Find the radius of the outer circle.
Now, we use the outer circumference, which is 308 m:
\[ 308 = 2\pi r_2 \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ 308 = 2 \times \frac{22}{7} \times r_2 \]
Simplifying the equation:
\[ 308 = \frac{44}{7} r_2 \]
Multiplying both sides by 7:
\[ 308 \times 7 = 44 r_2 \]
\[ 2156 = 44 r_2 \]
Now, divide both sides by 44:
\[ r_2 = \frac{2156}{44} = 49 \text{ m} \]

### Step 4: Calculate the width of the track.
The width of the racetrack is given by the difference between the outer radius and the inner radius:
\[ \text{Width} = r_2 - r_1 = 49 \text{ m} - 42 \text{ m} = 7 \text{ m} \]

### Final Answer:
The width of the racetrack is **7 meters**.

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