Question

Working together, Printer A and Printer B can print 60 pages in 10 minutes. Alone, it takes Printer B 15 minutes to print 45 pages. How long does it take Printer A to print 60 pages alone?

Answer 1

To find out how long it takes Printer A to print 60 pages alone, we first need to determine the printing rates of both Printer A and Printer B.

1. **Determine Printer B's Rate**:
Printer B takes 15 minutes to print 45 pages. Therefore, the rate of Printer B is:

\[
\text{Rate of Printer B} = \frac{45 \text{ pages}}{15 \text{ minutes}} = 3 \text{ pages per minute}
\]

2. **Determine the Combined Rate of Printer A and Printer B**:
Together, Printer A and Printer B can print 60 pages in 10 minutes. So, their combined rate is:

\[
\text{Combined Rate} = \frac{60 \text{ pages}}{10 \text{ minutes}} = 6 \text{ pages per minute}
\]

3. **Calculate Printer A's Rate**:
Let \( r_A \) be the rate of Printer A in pages per minute. According to the information we have:

\[
r_A + r_B = 6 \text{ pages per minute}
\]

We already know \( r_B = 3 \text{ pages per minute} \). Substituting \( r_B \) into the equation gives:

\[
r_A + 3 = 6
\]
\[
r_A = 6 - 3 = 3 \text{ pages per minute}
\]

4. **Finding the Time Taken by Printer A to Print 60 Pages**:
Now that we know the rate of Printer A, we can calculate how long it will take for Printer A to print 60 pages:

\[
\text{Time} = \frac{\text{Number of pages}}{\text{Rate}} = \frac{60 \text{ pages}}{3 \text{ pages per minute}} = 20 \text{ minutes}
\]

Therefore, it takes Printer A 20 minutes to print 60 pages alone.