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. can’t be determined

Answer

To solve the problem step by step, we will first determine the work done by the engineers and workers in the first scenario and then use that information to find out how many days it will take for the second scenario.

### Step 1: Determine the total work done in the first scenario
We know that:
- 20 engineers and 20 workers can construct a 20 km road in 20 days.

Total work done (in km) = 20 km
Total time taken = 20 days

### Step 2: Calculate the work done per day
The work done per day by 20 engineers and 20 workers:
\[ \text{Work per day} = \frac{\text{Total work}}{\text{Total time}} = \frac{20 \text{ km}}{20 \text{ days}} = 1 \text{ km/day} \]

### Step 3: Calculate the work done by one engineer and one worker
Since 20 engineers and 20 workers together do 1 km of work in a day, we can express this as:
\[ \text{Work done by 20 engineers and 20 workers in one day} = 1 \text{ km} \]

Let the work done by one engineer in one day be \( e \) km and the work done by one worker in one day be \( w \) km. Therefore:
\[ 20e + 20w = 1 \text{ km} \]
Dividing the entire equation by 20:
\[ e + w = \frac{1}{20} \text{ km} \]

### Step 4: Analyze the second scenario
Now, we need to find out how many days it will take for 40 engineers and 40 workers to construct a 40 km road.

Total work required = 40 km
Let \( d \) be the number of days required.

The work done by 40 engineers and 40 workers in one day:
\[ 40e + 40w \]
We can factor out 40:
\[ 40(e + w) = 40 \times \frac{1}{20} = 2 \text{ km/day} \]

### Step 5: Calculate the number of days required
Now, we need to find \( d \) such that:
\[ \text{Total work} = \text{Work done per day} \times \text{Number of days} \]
\[ 40 \text{ km} = 2 \text{ km/day} \times d \]
Solving for \( d \):
\[ d = \frac{40 \text{ km}}{2 \text{ km/day}} = 20 \text{ days} \]

### Final Answer
Thus, it will take 40 engineers and 40 workers **20 days** to construct a 40 km road.

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