Pipe A can fill a tank in 36 minutes and pipe B can fill it in 45 minutes. If both the pipes are opened to fill an empty tank, in how many minutes will it be full?

Options

A. 15
B. 18
C. 20
D. 25

Answer

To solve the problem of how long it will take for both Pipe A and Pipe B to fill the tank together, we can follow these steps:

### Step 1: Determine the rates of each pipe
- Pipe A can fill the tank in 36 minutes. Therefore, the rate of Pipe A is:
\[ \text{Rate of Pipe A} = \frac{1 \text{ tank}}{36 \text{ minutes}} = \frac{1}{36} \text{ tanks per minute} \]

- Pipe B can fill the tank in 45 minutes. Therefore, the rate of Pipe B is:
\[ \text{Rate of Pipe B} = \frac{1 \text{ tank}}{45 \text{ minutes}} = \frac{1}{45} \text{ tanks per minute} \]

### Step 2: Add the rates of both pipes
To find the combined rate when both pipes are opened together, we add their individual rates:
\[ \text{Combined Rate} = \text{Rate of Pipe A} + \text{Rate of Pipe B} = \frac{1}{36} + \frac{1}{45} \]

### Step 3: Find a common denominator
To add the fractions, we need a common denominator. The least common multiple (LCM) of 36 and 45 is 180. We convert each rate:
\[ \frac{1}{36} = \frac{5}{180} \quad \text{(since } 36 \times 5 = 180\text{)} \]
\[ \frac{1}{45} = \frac{4}{180} \quad \text{(since } 45 \times 4 = 180\text{)} \]

### Step 4: Add the fractions
Now we can add the two rates:
\[ \text{Combined Rate} = \frac{5}{180} + \frac{4}{180} = \frac{9}{180} = \frac{1}{20} \text{ tanks per minute} \]

### Step 5: Calculate the time to fill the tank
To find the time taken to fill one tank at the combined rate, we take the reciprocal of the combined rate:
\[ \text{Time} = \frac{1 \text{ tank}}{\frac{1}{20} \text{ tanks per minute}} = 20 \text{ minutes} \]

### Final Answer
Thus, if both pipes A and B are opened together, they will fill the tank in **20 minutes**.

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