Math Problem Statement

Meg is printing a term paper for class at the rate shown in the table below. If the term paper is 60 pages long, how many total minutes will it take to print out? Assume that the printer prints the pages at a constant rate.

Meg’s Term Paper Printing Progress Time (minutes) 3 4 5 6 7 Pages Printed 7.5 10 12.5 15 17.5

Solution

To solve this, we need to first find the rate at which Meg's printer prints pages per minute. We can use the data from the table to calculate this rate.

Step 1: Determine the rate of printing (pages per minute).

We will use two points from the table to calculate the rate. Let's choose the points for t=3t = 3 and t=4t = 4.

At t=3t = 3 minutes, Meg has printed 7.5 pages.
At t=4t = 4 minutes, Meg has printed 10 pages.

The change in the number of pages printed is:

ΔPages=107.5=2.5 pages\Delta \text{Pages} = 10 - 7.5 = 2.5 \text{ pages}

The change in time is:

ΔTime=43=1 minute\Delta \text{Time} = 4 - 3 = 1 \text{ minute}

So, the printer prints at a rate of:

Rate=2.5 pages1 minute=2.5 pages per minute\text{Rate} = \frac{2.5 \text{ pages}}{1 \text{ minute}} = 2.5 \text{ pages per minute}

Step 2: Find how long it takes to print 60 pages.

Now that we know the printer prints 2.5 pages per minute, we can calculate the time needed to print 60 pages. Using the formula:

Time=Total PagesRate\text{Time} = \frac{\text{Total Pages}}{\text{Rate}}

Substituting the values:

Time=60 pages2.5 pages per minute=24 minutes\text{Time} = \frac{60 \text{ pages}}{2.5 \text{ pages per minute}} = 24 \text{ minutes}

Conclusion:

It will take Meg 24 minutes to print her 60-page term paper.

Would you like more details or have any further questions?

Here are 5 related questions for practice:

  1. How many pages will the printer print in 10 minutes?
  2. If Meg only has 15 minutes to print, how many pages will she be able to print?
  3. What would the total time be if Meg’s term paper were 100 pages long?
  4. If the printer's rate increased to 3 pages per minute, how long would it take to print 60 pages?
  5. How many minutes would it take to print 30 pages at the current rate?

Tip: When working with rates, always confirm the units match before dividing or multiplying (e.g., pages per minute vs minutes per page).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Rate
Proportion
Division

Formulas

Rate = ΔPages / ΔTime
Time = Total Pages / Rate

Theorems

Concept of constant rate

Suitable Grade Level

Grades 6-8