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.
| Time (minutes) | 3 | 4 | 5 | 6 | 7 |
| :------------- | :-- | :- | :--- | :- | :--- |
| Pages Printed | 7.5 | 10 | 12.5 | 15 | 17.5 |
A. 20 minutes
B. 24 minutes
C. 150 minutes
Answer (2)
Calculate the printing rate: 3 7.5 = 2.5 pages per minute.
Set up the equation: 2.5 \t = 60 .
Solve for t : t = 2.5 60 = 24 .
The total time to print the term paper is 24 minutes.
Explanation
Understanding the Problem We are given a table that shows the number of pages Meg prints over a certain amount of time. We are asked to find how long it will take to print a 60-page term paper, assuming the printer prints at a constant rate.
Calculating the Printing Rate First, we need to find the rate at which Meg's printer prints. We can calculate this by dividing the number of pages printed by the time it takes to print them. From the table, we have the following data points:
3 minutes, 7.5 pages
4 minutes, 10 pages
5 minutes, 12.5 pages
6 minutes, 15 pages
7 minutes, 17.5 pages Let's calculate the printing rate using the first data point: 3 minutes 7.5 pages = 2.5 pages per minute We can verify that the rate is constant by calculating it for the other data points as well.
Calculating the Total Time Now that we know the printing rate is 2.5 pages per minute, we can find the time it takes to print a 60-page term paper. Let t be the time in minutes. We can set up the equation: 2.5 ⋅ t = 60 To solve for t , we divide both sides of the equation by 2.5: 2.5 2.5 ⋅ t = 2.5 60 t = 24 So it will take 24 minutes to print the 60-page term paper.
Final Answer Therefore, the total time it will take to print out the 60-page term paper is 24 minutes.
Examples
Imagine you are baking cookies for a bake sale. If you know that you can bake 10 cookies every 15 minutes, you can use this rate to calculate how long it will take to bake 50 cookies. This is a direct application of understanding rates and proportions, similar to the problem of Meg printing her term paper. By calculating the rate (cookies per minute) and then using that rate to determine the time needed for a larger batch, you can efficiently manage your baking schedule.
Meg will take 24 minutes to print her 60-page term paper. This is calculated based on her printer's rate of 2.5 pages per minute. Therefore, the answer is 24 minutes.
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