A pipe can fill an empty tank in 20 min and another pipe can fill it in 60 min. If both the pipes are kept open simultaneously, then in how many minutes will the tank get filled?

Answer

To solve the problem of how long it will take to fill the tank when both pipes are open simultaneously, we can follow these steps:

### Step 1: Determine the rates of each pipe.
- The first pipe can fill the tank in 20 minutes. Therefore, its rate is:
\[ \text{Rate of Pipe A} = \frac{1 \text{ tank}}{20 \text{ minutes}} = \frac{1}{20} \text{ tanks per minute} \]
- The second pipe can fill the tank in 60 minutes. Therefore, its rate is:
\[ \text{Rate of Pipe B} = \frac{1 \text{ tank}}{60 \text{ minutes}} = \frac{1}{60} \text{ tanks per minute} \]

### Step 2: Add the rates of both pipes.
- When both pipes are open, their combined rate is:
\[ \text{Combined Rate} = \text{Rate of Pipe A} + \text{Rate of Pipe B} = \frac{1}{20} + \frac{1}{60} \]

### Step 3: Find a common denominator to add the fractions.
- The least common multiple (LCM) of 20 and 60 is 60. We can rewrite the first fraction:
\[ \frac{1}{20} = \frac{3}{60} \]
- Now we can add the two rates:
\[ \text{Combined Rate} = \frac{3}{60} + \frac{1}{60} = \frac{4}{60} = \frac{1}{15} \text{ tanks per minute} \]

### Step 4: Calculate the time taken to fill the tank.
- Since the combined rate is \(\frac{1}{15}\) tanks per minute, it means that together both pipes can fill 1 tank in 15 minutes.

Thus, the tank will get filled in **15 minutes**.

### Final Answer:
The tank will be filled in **15 minutes**.

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