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Answer :
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.
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.
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