Calculate Swimming Speed: Converting 22½ Meters per 7 Seconds

Let's solve the problem step-by-step:

Step 1: Convert the mixed fraction to an improper fraction.
The mixed number $22\frac{1}{2}$ can be expressed in terms of improper fraction as follows:
First, convert $22\frac{1}{2}$ to an improper fraction:
$22\frac{1}{2} = \frac{2 \times 22 + 1}{2} = \frac{45}{2}$.

Step 2: Use the speed formula.
We know that speed = distance / time. Here, the distance is $\frac{45}{2}$ meters and the time is 7 seconds.
To find meters per second, we calculate:
$\frac{45}{2} \div 7 = \frac{45}{2} \times \frac{1}{7} = \frac{45}{14}$.

Step 3: Simplify the fraction.
The fraction $\frac{45}{14}$ can be simplified. It converts to mixed number as follows:
First, divide 45 by 14 which gives a quotient of 3 and a remainder of 3.
Therefore, $\frac{45}{14} = 3\frac{3}{14}$.

Therefore, Daniel swims $3\frac{3}{14}$ meters per second.