If 14 workers can build a wall in 45 hours, how many workers will be required to do the same work in 35 hours?

Answer

To solve the problem step by step, we will use the concept of inverse proportion.

### Step 1: Understand the relationship
We know that if the time taken to complete a task decreases, the number of workers required to complete the same task increases. This is an example of inverse proportion.

**Hint:** Remember that in inverse proportion, if one quantity increases, the other must decrease, and vice versa.

### Step 2: Set up the proportion
Given:
- 14 workers can build a wall in 45 hours.
- We need to find out how many workers (let's call it W) are required to build the same wall in 35 hours.

### Step 3: Use the inverse proportion formula
Using the formula for inverse proportion:
\[ \text{Workers} \times \text{Time} = \text{Constant} \]
We can set up the equation:
\[ 14 \text{ workers} \times 45 \text{ hours} = W \text{ workers} \times 35 \text{ hours} \]

### Step 4: Calculate the constant
First, calculate the constant:
\[ 14 \times 45 = 630 \]

### Step 5: Set up the equation with the constant
Now we can rewrite the equation using the constant:
\[ 630 = W \times 35 \]

### Step 6: Solve for W
To find W, divide both sides of the equation by 35:
\[ W = \frac{630}{35} \]

### Step 7: Perform the division
Now, calculate the value:
\[ W = 18 \]

### Conclusion
Therefore, **18 workers** will be required to build the wall in 35 hours.

**Final Answer:** 18 workers

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