If 36 men can build a wall of 140 m length in 10.5 days, how many men could take 9 days to build a similar type of wall of length 50 m?

Answer

To solve the problem step by step, we will use the chain rule formula, which relates the number of men, the number of days, and the amount of work done.

### Step 1: Understand the given information
We know that:
- 36 men can build a wall of 140 meters in 10.5 days.
- We need to find out how many men (let's call this \( m_2 \)) are required to build a wall of 50 meters in 9 days.

### Step 2: Define the variables
Let:
- \( m_1 = 36 \) (the number of men in the first scenario)
- \( d_1 = 10.5 \) (the number of days in the first scenario)
- \( w_1 = 140 \) (the length of the wall in the first scenario)
- \( d_2 = 9 \) (the number of days in the second scenario)
- \( w_2 = 50 \) (the length of the wall in the second scenario)
- \( m_2 \) (the number of men we need to find)

### Step 3: Use the chain rule formula
The chain rule states:
\[ \frac{m_1 \cdot d_1}{w_1} = \frac{m_2 \cdot d_2}{w_2} \]

### Step 4: Substitute the known values into the formula
Substituting the known values into the formula, we get:
\[ \frac{36 \cdot 10.5}{140} = \frac{m_2 \cdot 9}{50} \]

### Step 5: Simplify the left side of the equation
Calculating the left side:
\[ 36 \cdot 10.5 = 378 \]
So,
\[ \frac{378}{140} = \frac{m_2 \cdot 9}{50} \]

### Step 6: Cross-multiply to solve for \( m_2 \)
Cross-multiplying gives us:
\[ 378 \cdot 50 = 140 \cdot m_2 \cdot 9 \]
Calculating \( 378 \cdot 50 \):
\[ 18900 = 140 \cdot m_2 \cdot 9 \]

### Step 7: Simplify the equation
Now, simplify the right side:
\[ 18900 = 1260 \cdot m_2 \]

### Step 8: Solve for \( m_2 \)
Now, divide both sides by 1260 to find \( m_2 \):
\[ m_2 = \frac{18900}{1260} \]
Calculating this gives:
\[ m_2 = 15 \]

### Conclusion
Thus, the number of men required to build a wall of 50 meters in 9 days is **15 men**.

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