Karen can read 10 pages and complete 15 math problems in 30 minutes. How long will it take her to do her homework if she has 30 pages to read and 45 math problems to complete? Your answer should refer to the amount of time in minutes.(1 point)
To find out how long it will take Karen to do her homework, we need to determine the time it takes her to complete each page and math problem.
First, let's calculate the time it takes Karen to complete one page. We know that she can read 10 pages in 30 minutes, so we can set up a proportion:
10 pages / 30 minutes = 1 page / x minutes
Cross-multiplying, we get:
10x = 30
x = 30 / 10
x = 3 minutes
So, it takes Karen 3 minutes to read one page.
Next, let's calculate the time it takes Karen to complete one math problem. We know that she can complete 15 math problems in 30 minutes, so we can set up another proportion:
15 problems / 30 minutes = 1 problem / y minutes
Cross-multiplying, we get:
15y = 30
y = 30 / 15
y = 2 minutes
So, it takes Karen 2 minutes to complete one math problem.
Now that we know the time it takes Karen to complete one page and one math problem, we can calculate the total time it will take for her to complete her homework.
Reading 30 pages at a rate of 3 minutes per page will take Karen:
30 pages * 3 minutes per page = 90 minutes
Completing 45 math problems at a rate of 2 minutes per problem will take Karen:
45 problems * 2 minutes per problem = 90 minutes
Therefore, it will take Karen a total of 90 minutes + 90 minutes = 180 minutes, or 3 hours, to do her homework.
We can set up a proportion to solve this problem:
10 pages / 15 problems = 30 minutes / x minutes (where x is the time it takes Karen to do her homework)
Now we can cross-multiply and solve for x:
10x = 15 * 30
10x = 450
x = 450 / 10
x = 45
So, it will take Karen 45 minutes to do her homework.
To find out how long it will take Karen to do her homework, we need to determine the amount of time she takes to complete each page of reading and each math problem.
First, let's find the time it takes for Karen to read each page:
She can read 10 pages in 30 minutes, so the time taken for 1 page is 30 minutes / 10 pages = 3 minutes per page.
Next, let's find the time it takes for Karen to complete each math problem:
She can complete 15 math problems in 30 minutes, so the time taken for 1 math problem is 30 minutes / 15 problems = 2 minutes per math problem.
Now, let's calculate the total time it will take for Karen to do her homework:
For reading 30 pages: 30 pages * 3 minutes per page = 90 minutes.
For completing 45 math problems: 45 problems * 2 minutes per math problem = 90 minutes.
Finally, to find the total time, we add the time for reading the pages and completing the math problems:
Total time = 90 minutes (reading) + 90 minutes (math problems) = 180 minutes.
Therefore, it will take Karen 180 minutes to do her homework.