The amount of time it takes to consume a buffalo carcass is inversely proportional to the number of vultures. IF it takes 12 vultures 3 day to consume a buffalo, how many fewer hours will it take there are 4 more vultures?

Options

A. `1/4`
B. `3/4`
C. 18
D. 54

Answer

To solve the problem, we need to follow these steps:

### Step 1: Understand the relationship
The time taken to consume a buffalo carcass (t) is inversely proportional to the number of vultures (v). This can be expressed mathematically as:
\[ t \propto \frac{1}{v} \]
This means:
\[ t = \frac{k}{v} \]
where \( k \) is a constant.

### Step 2: Find the constant \( k \)
We know that 12 vultures take 3 days to consume a buffalo. We can substitute these values into the equation to find \( k \):
\[ t = 3 \text{ days} \]
\[ v = 12 \]
Substituting these into the equation:
\[ 3 = \frac{k}{12} \]
To find \( k \), we multiply both sides by 12:
\[ k = 3 \times 12 = 36 \]

### Step 3: Calculate time with 16 vultures
Now we need to find out how much time it takes with 4 more vultures, which means we will have 16 vultures (12 + 4). We can use the constant \( k \) we found:
\[ t = \frac{k}{v} = \frac{36}{16} \]
Calculating this gives:
\[ t = 2.25 \text{ days} \]

### Step 4: Convert days to hours
Since we need the answer in hours, we convert days to hours:
\[ t = 2.25 \text{ days} \times 24 \text{ hours/day} = 54 \text{ hours} \]

### Step 5: Calculate the time with 12 vultures
Next, we need to find out how many hours it took with 12 vultures:
\[ t = 3 \text{ days} \]
Converting this to hours:
\[ t = 3 \text{ days} \times 24 \text{ hours/day} = 72 \text{ hours} \]

### Step 6: Find the difference in hours
Finally, we find how many fewer hours it takes with 16 vultures compared to 12 vultures:
\[ \text{Difference} = 72 \text{ hours} - 54 \text{ hours} = 18 \text{ hours} \]

### Final Answer
Thus, it takes **18 fewer hours** when there are 4 more vultures.

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