If 56 workers can build a wall in 180 hours, how many workers will be required to do the same work in 70 hours ?

Answer

To solve the problem step by step, we can use the concept of inverse variation. Here's how to approach it:

### Step 1: Understand the relationship
We know that the amount of work done is constant. Therefore, if the time taken decreases, the number of workers required must increase. This indicates an inverse relationship between the number of workers and the time taken.

### Step 2: Set up the equation
Let \( x \) be the number of workers required to build the wall in 70 hours. According to the problem, we can set up the relationship as follows:
\[ 56 \text{ workers} \times 180 \text{ hours} = x \text{ workers} \times 70 \text{ hours} \]

### Step 3: Rearrange the equation
We can rearrange the equation to solve for \( x \):
\[ x = \frac{56 \times 180}{70} \]

### Step 4: Simplify the equation
Now we can simplify the right side of the equation:
1. First, calculate \( 56 \times 180 \):
\[ 56 \times 180 = 10080 \]
2. Now divide by 70:
\[ x = \frac{10080}{70} \]

### Step 5: Perform the division
Now we can perform the division:
\[ x = 144 \]

### Conclusion
Thus, the number of workers required to build the wall in 70 hours is \( 144 \).