14 horses can consume a certain quantitiy of corn in 25 days.In how many days would the same quantity be consumed by 40 horses?

Answer

To solve the problem step by step using the unitary method, we can follow these steps:

### Step 1: Determine the total quantity of corn consumed by 14 horses in 25 days.
- We know that 14 horses consume a certain quantity of corn in 25 days.
- To find the total quantity of corn consumed, we multiply the number of horses by the number of days:
\[ \text{Total quantity of corn} = 14 \text{ horses} \times 25 \text{ days} = 350 \text{ horse-days} \]

### Step 2: Set up the equation for 40 horses.
- Now we need to find out how many days it would take for 40 horses to consume the same quantity of corn (350 horse-days).
- Let \( x \) be the number of days it takes for 40 horses to consume the same quantity of corn.

### Step 3: Write the equation.
- The total corn consumed by 40 horses in \( x \) days can be expressed as:
\[ \text{Total quantity of corn} = 40 \text{ horses} \times x \text{ days} \]
- Since both expressions represent the same total quantity of corn, we can set them equal to each other:
\[ 40x = 350 \]

### Step 4: Solve for \( x \).
- To find \( x \), divide both sides of the equation by 40:
\[ x = \frac{350}{40} \]
- Simplifying this fraction gives:
\[ x = \frac{35}{4} = 8.75 \]

### Step 5: Conclusion.
- Therefore, it will take 40 horses 8.75 days to consume the same quantity of corn.

### Final Answer:
- **40 horses will take 8.75 days to consume the same quantity of corn.**

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