24 men working 8 hours a day make a road in 15 days. In how many days 48 men working 6 hours a day will make the three times long road?

Answer

To solve the problem step by step, we will use the concept of work done, which is calculated as:

\[ \text{Work} = \text{Number of Men} \times \text{Number of Days} \times \text{Number of Hours per Day} \]

### Step 1: Calculate the total work done by the first group of men
Given:
- Number of men (P1) = 24
- Number of days (D1) = 15
- Number of hours per day (H1) = 8

Using the formula for work:

\[ W1 = P1 \times D1 \times H1 = 24 \times 15 \times 8 \]

Calculating this:

\[ W1 = 24 \times 15 = 360 \]
\[ W1 = 360 \times 8 = 2880 \text{ man-hours} \]

### Step 2: Calculate the total work for the new scenario
The new scenario involves making a road that is three times longer than the original road. Therefore, the total work required (W2) will be:

\[ W2 = 3 \times W1 = 3 \times 2880 = 8640 \text{ man-hours} \]

### Step 3: Set up the equation for the second group of men
Now we need to find out how many days (D2) it will take for 48 men working 6 hours a day to complete this work.

Given:
- Number of men (P2) = 48
- Number of hours per day (H2) = 6

Using the work formula again, we have:

\[ W2 = P2 \times D2 \times H2 \]

Substituting the known values:

\[ 8640 = 48 \times D2 \times 6 \]

### Step 4: Solve for D2
First, calculate \(48 \times 6\):

\[ 48 \times 6 = 288 \]

Now substitute this back into the equation:

\[ 8640 = 288 \times D2 \]

To find \(D2\), divide both sides by 288:

\[ D2 = \frac{8640}{288} \]

Calculating this gives:

\[ D2 = 30 \]

### Final Answer
Thus, it will take **30 days** for 48 men working 6 hours a day to make the three times long road.

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