An above-ground swimming pool is leaking. After [tex]\frac{1}{2}[/tex] hour, the pool has leaked [tex]\frac{7}{8}[/tex] of a gallon of water. How many gallons of water per hour is the swimming pool leaking?

To determine the rate at which the swimming pool is leaking water, follow these steps:

1. Identify the given quantities:
- Time interval: [tex]$\frac{1}{2}$[/tex] hour
- Amount of water leaked in that time: [tex]$\frac{7}{8}$[/tex] gallon

2. Determine the leaking rate in gallons per hour:
- The leaking rate can be calculated using the formula:
[tex]\[
\text{Leaking Rate} = \frac{\text{Amount of water leaked}}{\text{Time interval}}
\][/tex]

3. Plug in the given values:
- Substitute the given values into the formula:
[tex]\[
\text{Leaking Rate} = \frac{\frac{7}{8} \text{ gallon}}{\frac{1}{2} \text{ hour}}
\][/tex]

4. Solve the division of fractions:
- Dividing by a fraction is the same as multiplying by its reciprocal. So, divide [tex]$\frac{7}{8}$[/tex] gallon by [tex]$\frac{1}{2}$[/tex] hour:
[tex]\[
\text{Leaking Rate} = \frac{7}{8} \div \frac{1}{2} = \frac{7}{8} \times \frac{2}{1} = \frac{7 \times 2}{8 \times 1} = \frac{14}{8} = 1.75 \text{ gallons per hour}
\][/tex]

Therefore, the swimming pool is leaking water at a rate of 1.75 gallons per hour.