The amount of time it take to consume a buffalo carcasess is inversly proporation to the number of vultures. If it takes 12 vultures 3 days to consume a buffalo, how many fewer hours will it take if there are 4 more vultures?

Options

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

Answer

To solve the problem, we need to use the concept of inverse proportionality between the number of vultures and the time taken to consume a buffalo carcass. Here’s the step-by-step solution:

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

### Step 2: Determine the constant
From the problem, we know that 12 vultures take 3 days to consume a buffalo. First, we need to convert days into hours:
\[ 3 \text{ days} = 3 \times 24 = 72 \text{ hours} \]

Now we can find the constant \( k \):
\[ T \times V = k \]
\[ 72 \text{ hours} \times 12 \text{ vultures} = k \]
\[ k = 864 \]

### Step 3: Calculate time for 16 vultures
Now we need to find out how long it will take for 16 vultures to consume the buffalo. Using the constant \( k \):
\[ T \times 16 = 864 \]
\[ T = \frac{864}{16} \]
\[ T = 54 \text{ hours} \]

### Step 4: Find the difference in time
Now we need to find out how many fewer hours it takes with 16 vultures compared to 12 vultures:
\[ \text{Time with 12 vultures} = 72 \text{ hours} \]
\[ \text{Time with 16 vultures} = 54 \text{ hours} \]
The difference is:
\[ 72 - 54 = 18 \text{ hours} \]

### Conclusion
Therefore, it will take 18 fewer hours to consume the buffalo carcass with 4 more vultures.

### Final Answer
**18 hours**

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