Twelve typists, all working with same speed, type a certain number of pages in 18 days working 8 hours a day. Find, how many hours per day must sixteen typists work in order to type the same number of pages in 9 days ?

Answer

To solve the problem step by step, we will use the concept of work done, which is given by the formula:

**Work = Number of Typists × Hours per Day × Number of Days**

### Step 1: Calculate the total work done by 12 typists.
- Given:
- Number of typists = 12
- Hours per day = 8
- Days = 18

Using the formula:
\[ \text{Total Work} = 12 \text{ typists} \times 8 \text{ hours/day} \times 18 \text{ days} \]

Calculating:
\[ \text{Total Work} = 12 \times 8 \times 18 \]
\[ = 12 \times 144 \]
\[ = 1728 \text{ typist-hours} \]

### Step 2: Set up the equation for the work done by 16 typists.
- We need to find how many hours per day (let's denote it as \( x \)) 16 typists must work to complete the same amount of work in 9 days.

Using the same formula:
\[ \text{Total Work} = 16 \text{ typists} \times x \text{ hours/day} \times 9 \text{ days} \]

### Step 3: Set the two expressions for work equal to each other.
Since both expressions represent the same total work:
\[ 12 \times 8 \times 18 = 16 \times x \times 9 \]

Substituting the total work calculated in Step 1:
\[ 1728 = 16 \times x \times 9 \]

### Step 4: Simplify the equation.
First, simplify the right side:
\[ 1728 = 144x \]

### Step 5: Solve for \( x \).
To find \( x \), divide both sides by 144:
\[ x = \frac{1728}{144} \]

Calculating:
\[ x = 12 \]

### Conclusion:
The number of hours per day that 16 typists must work is **12 hours**.

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