If 20 engineers and 20 workers can together construct a 20 km road in 20 days. 40 engineers and 40 workers together construct 40 km road in how many days?

Options

A. 10
B. 20
C. 40
D. none of the above

Answer

To solve the problem step by step, we will use the relationship between the number of workers, the distance to be constructed, and the time taken.

### Step 1: Understand the given information
We know that:
- 20 engineers and 20 workers can construct a 20 km road in 20 days.

### Step 2: Establish the relationship using the chain rule
We can use the formula:
\[ \frac{m_1 \cdot d_1}{w_1} = \frac{m_2 \cdot d_2}{w_2} \]
Where:
- \( m_1 \) = number of workers in the first scenario (20 engineers + 20 workers = 40)
- \( d_1 \) = distance in the first scenario (20 km)
- \( w_1 \) = time in the first scenario (20 days)
- \( m_2 \) = number of workers in the second scenario (40 engineers + 40 workers = 80)
- \( d_2 \) = distance in the second scenario (40 km)
- \( w_2 \) = time in the second scenario (which we need to find, let's call it \( x \))

### Step 3: Substitute the known values into the formula
Substituting the values into the formula, we get:
\[ \frac{40 \cdot 20}{20} = \frac{80 \cdot 40}{x} \]

### Step 4: Simplify the equation
The left side simplifies to:
\[ \frac{40 \cdot 20}{20} = 40 \]
So we have:
\[ 40 = \frac{80 \cdot 40}{x} \]

### Step 5: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 40x = 80 \cdot 40 \]
This simplifies to:
\[ 40x = 3200 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 40:
\[ x = \frac{3200}{40} = 80 \]

### Conclusion
Thus, 40 engineers and 40 workers can construct a 40 km road in **80 days**.