it takes 30 minutes for 5 old printers to produce a batch of magazines.it takes 16 minutes for 4 new printers to produce an identical batch of magazines.Wich of the following magazines would produce a batch of magazines in less time?

To solve this, let's calculate the rate at which both the old and new printers produce magazines, then compare their speeds to determine which set of printers would finish the task in less time.

### Step 1: Calculate the rate of the old printers.
- 5 old printers take 30 minutes to produce 1 batch.
- So, the time for 1 old printer to produce 1 batch would be: 
\[
5 \text{ printers} \times 30 \text{ minutes} = 150 \text{ minutes}
\]
1 old printer would take 150 minutes to produce a batch, so the rate of 1 old printer is:
\[
\frac{1 \text{ batch}}{150 \text{ minutes}} = \frac{1}{150} \text{ batches per minute}.
\]
For 5 old printers, the rate is:
\[
5 \times \frac{1}{150} = \frac{5}{150} = \frac{1}{30} \text{ batches per minute}.
\]

### Step 2: Calculate the rate of the new printers.
- 4 new printers take 16 minutes to produce 1 batch.
- The time for 1 new printer to produce 1 batch would be:
\[
4 \text{ printers} \times 16 \text{ minutes} = 64 \text{ minutes}.
\]
1 new printer would take 64 minutes to produce a batch, so the rate of 1 new printer is:
\[
\frac{1 \text{ batch}}{64 \text{ minutes}} = \frac{1}{64} \text{ batches per minute}.
\]
For 4 new printers, the rate is:
\[
4 \times \frac{1}{64} = \frac{4}{64} = \frac{1}{16} \text{ batches per minute}.
\]

### Step 3: Compare the rates.
- 5 old printers produce at a rate of \(\frac{1}{30}\) batches per minute.
- 4 new printers produce at a rate of \(\frac{1}{16}\) batches per minute.

Since \(\frac{1}{16} > \frac{1}{30}\), the new printers produce batches at a faster rate than the old printers.

### Conclusion:
The **new printers** would produce a batch of magazines in less time than the old printers.

Would you like more details or have any further questions?

Here are some related questions you might explore:
1. How long would it take 3 new printers to produce 2 batches of magazines?
2. How many old printers would be needed to match the speed of 4 new printers?
3. If 1 new printer is removed, how long would it take for the remaining 3 printers to finish a batch?
4. What is the combined rate if both old and new printers work together on a batch?
5. How many new printers would be needed to produce a batch in 10 minutes?

**Tip:** When comparing work rates, it's useful to calculate how much of the task can be completed per minute for each group or individual.

It takes 30 minutes for 5 old printers to produce a batch of magazines. It takes 16 minutes for 4 new printers to produce an identical batch of magazines. Which of the following printers would produce a batch of magazines in less time?

Learn how to compare the work rates of 5 old printers and 4 new printers to determine which group produces a batch of magazines in less time. This problem demonstrates the concepts of work rates and proportionality, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation