It took 64 people 77 days to construct a house. What fraction of the work can be completed by 44 people in 96 days?

Options

A. `(3)/(4)`
B. `(4)/(5)`
C. `(6)/(7)`
D. `(2)/(3)`

Answer

To solve the problem step by step, we will calculate the total work done by the first group of people and then determine how much work can be done by the second group of people. Finally, we will find the fraction of work completed.

### Step 1: Calculate the total work done by 64 people in 77 days.
The total work can be calculated using the formula:
\[ \text{Total Work} = \text{Number of People} \times \text{Number of Days} \]
So, for 64 people working for 77 days:
\[ \text{Total Work} = 64 \times 77 \]

### Step 2: Calculate the work done by 44 people in 96 days.
Using the same formula for the second group:
\[ \text{Work Done by 44 People} = 44 \times 96 \]

### Step 3: Set up the fraction of work completed.
The fraction of work completed by 44 people in 96 days compared to the total work is given by:
\[ \text{Fraction of Work} = \frac{\text{Work Done by 44 People}}{\text{Total Work}} \]
Substituting the values from Steps 1 and 2:
\[ \text{Fraction of Work} = \frac{44 \times 96}{64 \times 77} \]

### Step 4: Simplify the fraction.
We can simplify the fraction by canceling out common factors:
1. \( 44 \) and \( 64 \) can be simplified by dividing both by \( 4 \):
- \( 44 \div 4 = 11 \)
- \( 64 \div 4 = 16 \)

2. Now the fraction looks like:
\[ \frac{11 \times 96}{16 \times 77} \]

3. Next, we can simplify \( 96 \) and \( 16 \) by dividing both by \( 16 \):
- \( 96 \div 16 = 6 \)

4. Now the fraction looks like:
\[ \frac{11 \times 6}{77} \]

5. Finally, simplify \( 11 \) and \( 77 \) by dividing both by \( 11 \):
- \( 77 \div 11 = 7 \)

Now we have:
\[ \frac{6}{7} \]

### Final Answer:
The fraction of the work that can be completed by 44 people in 96 days is \( \frac{6}{7} \).

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