Because of anticipated heavy rain , the water level in a swimming pool must be lowered by 1 foot . Opening drain A lowers the level by 1 foot in 4 hours , whereas opening the smaller drain B does the job in 6 hours . How long will it take to lower the water level by 1 foot if both drains are opended ?
An equation that solves the problem is

Options

A. `1/4+1/6=1/x`
B. `4/x+6/x=1`
C. `x/4+x/6=x-1`
D. `1/4+1/6=x`

Answer

To solve the problem of how long it will take to lower the water level in the swimming pool by 1 foot when both drains A and B are opened, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the rates of work for each drain:**
- Drain A lowers the water level by 1 foot in 4 hours. Therefore, the rate of work for drain A is:
\[ \text{Rate of A} = \frac{1 \text{ foot}}{4 \text{ hours}} = \frac{1}{4} \text{ feet per hour} \]
- Drain B lowers the water level by 1 foot in 6 hours. Therefore, the rate of work for drain B is:
\[ \text{Rate of B} = \frac{1 \text{ foot}}{6 \text{ hours}} = \frac{1}{6} \text{ feet per hour} \]

2. **Combine the rates of work:**
- When both drains are opened, their combined rate of work is the sum of their individual rates:
\[ \text{Combined Rate} = \text{Rate of A} + \text{Rate of B} = \frac{1}{4} + \frac{1}{6} \]

3. **Find a common denominator to add the fractions:**
- The least common multiple of 4 and 6 is 12. Therefore, we convert the fractions:
\[ \frac{1}{4} = \frac{3}{12} \quad \text{and} \quad \frac{1}{6} = \frac{2}{12} \]
- Now we can add them:
\[ \text{Combined Rate} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \text{ feet per hour} \]

4. **Set up the equation for the total work:**
- Let \( x \) be the time in hours it takes to lower the water level by 1 foot when both drains are opened. The equation based on the combined rate is:
\[ \frac{5}{12} \cdot x = 1 \text{ foot} \]

5. **Solve for \( x \):**
- Rearranging the equation gives:
\[ x = \frac{1}{\frac{5}{12}} = \frac{12}{5} = 2.4 \text{ hours} \]

### Final Answer:
It will take **2.4 hours** to lower the water level by 1 foot if both drains A and B are opened.

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