Find the unit rate. $$ 21 \frac{3}{4} $$ meters in $$ 2 \frac{1}{2} $$ hours The unit rate is $$ \square $$ meters per hour.

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We are given a distance of $$21\frac{3}{4}$$ meters covered in $$2\frac{1}{2}$$ hours. We need to find the unit rate in meters per hour.

1. **Convert the mixed numbers to improper fractions:**

- For the distance:
     $$
     21\frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4}
     $$
     
   - For the time:
     $$
     2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}
     $$

2. **Divide the distance by the time:**
   
   $$
   \text{Unit Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{87}{4}}{\frac{5}{2}}
   $$

3. **Simplify the division by multiplying by the reciprocal:**

$$
   \frac{\frac{87}{4}}{\frac{5}{2}} = \frac{87}{4} \times \frac{2}{5} = \frac{87 \times 2}{4 \times 5} = \frac{174}{20}
   $$

4. **Simplify the fraction:**

Divide numerator and denominator by 2:
   $$
   \frac{174}{20} = \frac{87}{10}
   $$

Thus, the unit rate is:
$$
\boxed{\frac{87}{10}}
$$
meters per hour.
The unit rate is $$ \frac{87}{10} $$ meters per hour.

Find the unit rate. \( 21 \frac{3}{4} \) meters in \( 2 \frac{1}{2} \) hours The unit rate is \( \square \) meters per hour.

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