A new printing press can print 5,000 flyers in half the amount of time it take for an older printing press the same 5,000 flayers. Working together, the two printing presses can complete the entire job in 3 hours. How long would it take the faster printing press working alone to complete the job?

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Define the time taken by the older printing press
Let the time taken by the older printing press to print 5,000 flyers be \( x \) hours.

### Step 2: Determine the time taken by the new printing press
Since the new printing press takes half the time of the older printing press, the time taken by the new printing press will be:
\[ \frac{x}{2} \text{ hours} \]

### Step 3: Calculate the work done by each press in one hour
- The work done by the older printing press in one hour is:
\[ \frac{1}{x} \text{ of the work} \]
- The work done by the new printing press in one hour is:
\[ \frac{2}{x} \text{ of the work} \]

### Step 4: Combine the work done by both presses in one hour
When both presses work together, the total work done in one hour is:
\[ \frac{1}{x} + \frac{2}{x} = \frac{3}{x} \]

### Step 5: Relate the combined work to the time taken together
According to the problem, when both presses work together, they complete the entire job in 3 hours. Therefore, in one hour, they complete:
\[ \frac{1}{3} \text{ of the work} \]
This gives us the equation:
\[ \frac{3}{x} = \frac{1}{3} \]

### Step 6: Solve for \( x \)
To solve for \( x \), we cross-multiply:
\[ 3 \cdot 3 = 1 \cdot x \implies 9 = x \]
Thus, the older printing press takes \( 9 \) hours to complete the job.

### Step 7: Determine the time taken by the new printing press
Now, we can find the time taken by the new printing press:
\[ \frac{x}{2} = \frac{9}{2} = 4.5 \text{ hours} \]

### Final Answer
The faster printing press (the new printing press) would take **4.5 hours** to complete the job working alone.

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