12 pipes, all of the same size, fill a tank in 42 minutes. How long will it take to fill the same tank,if 21 pipes of the same size are used ?

Answer

To solve the problem step by step, we can use the concept of direct variation. The number of pipes and the time taken to fill the tank are inversely related. This means that as the number of pipes increases, the time taken to fill the tank decreases.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Number of pipes = 12
- Time taken to fill the tank with 12 pipes = 42 minutes

2. **Set Up the Relationship**:
- Let the time taken to fill the tank with 21 pipes be \( x \) minutes.
- Since the number of pipes and time are inversely related, we can set up the equation:
\[ 12 \times 42 = 21 \times x \]

3. **Substitute the Values**:
- Now substitute the known values into the equation:
\[ 504 = 21x \]
(Here, \( 12 \times 42 = 504 \))

4. **Solve for \( x \)**:
- To find \( x \), divide both sides of the equation by 21:
\[ x = \frac{504}{21} \]

5. **Calculate the Value**:
- Perform the division:
\[ x = 24 \]

6. **Conclusion**:
- Therefore, it will take 24 minutes to fill the tank with 21 pipes.

### Final Answer:
It will take **24 minutes** to fill the tank if 21 pipes of the same size are used.

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