Pipe A can fill a tank in 30 minutes. Pipe B can fill the same tank in 50 minutes. In how much time (in minutes) both pipes together can fill the same tank?

Options

A. 15.25
B. 22.5
C. 18.75
D. 20

Answer

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

### Step 1: Determine the rate of each pipe
- **Pipe A** fills the tank in 30 minutes. Therefore, in one minute, it fills:
\[ \text{Rate of Pipe A} = \frac{1}{30} \text{ tanks per minute} \]

- **Pipe B** fills the tank in 50 minutes. Therefore, in one minute, it fills:
\[ \text{Rate of Pipe B} = \frac{1}{50} \text{ tanks per minute} \]

### Step 2: Calculate the combined rate of both pipes
To find the combined rate when both pipes are working together, we add their individual rates:
\[ \text{Combined Rate} = \text{Rate of Pipe A} + \text{Rate of Pipe B} = \frac{1}{30} + \frac{1}{50} \]

### Step 3: Find a common denominator
The least common multiple (LCM) of 30 and 50 is 150. We convert the rates to have a common denominator:
\[ \frac{1}{30} = \frac{5}{150}, \quad \frac{1}{50} = \frac{3}{150} \]
Now, we can add them:
\[ \text{Combined Rate} = \frac{5}{150} + \frac{3}{150} = \frac{8}{150} = \frac{4}{75} \text{ tanks per minute} \]

### Step 4: Calculate the time taken to fill one tank
To find the time taken to fill one tank, we take the reciprocal of the combined rate:
\[ \text{Time} = \frac{1 \text{ tank}}{\frac{4}{75} \text{ tanks per minute}} = \frac{75}{4} \text{ minutes} \]

### Step 5: Convert the time into minutes and seconds
Calculating \( \frac{75}{4} \):
\[ \frac{75}{4} = 18.75 \text{ minutes} \]
This can be converted to minutes and seconds:
- 18 minutes and \( 0.75 \times 60 = 45 \) seconds.

### Final Answer
Thus, both pipes together can fill the tank in **18 minutes and 45 seconds**.

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