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)
minutes
If Karen can read 10 pages and complete 15 math problems in 30 minutes, then in 30 minutes she can read 10/30 = 1/3 of a page per minute.
In the same amount of time, she can complete 15/30 = 1/2 of a math problem per minute.
Since she has 30 pages to read, it will take her (30 * 3) = 90 minutes to read all the pages.
Since she has 45 math problems to complete, it will take her (45 * 2) = 90 minutes to complete all the math problems.
Therefore, it will take Karen 90 minutes to complete her homework.
To find out how long it will take Karen to do her homework, we can use the information given. We know that she can read 10 pages and complete 15 math problems in 30 minutes.
To determine the ratio of pages read to minutes, we divide the number of pages by the time taken:
10 pages / 30 minutes = 1/3 pages per minute.
Similarly, to find the ratio of math problems completed to minutes, we divide the number of problems by the time taken:
15 math problems / 30 minutes = 1/2 problems per minute.
Now, we can calculate the time it will take her to read 30 pages:
30 pages * (1/3 pages per minute) = 10 minutes.
And the time it will take her to complete 45 math problems:
45 math problems * (1/2 problems per minute) = 22.5 minutes.
To find the total time required for her homework, we add the time for reading and math:
10 minutes (reading) + 22.5 minutes (math) = 32.5 minutes.
Therefore, it will take Karen 32.5 minutes to complete her homework.
To solve this problem, we need to find the amount of time it will take Karen to complete both her reading and math homework. Here's how we can approach it:
1. First, let's determine Karen's reading speed. We know that Karen can read 10 pages in 30 minutes. Therefore, her reading speed is 10 pages / 30 minutes = 1/3 pages per minute.
2. Next, let's determine Karen's math problem-solving speed. We know that Karen can complete 15 math problems in 30 minutes. Therefore, her math problem-solving speed is 15 problems / 30 minutes = 1/2 problems per minute.
3. Now, let's find how long it will take Karen to complete her reading homework. Karen has 30 pages to read, and her reading speed is 1/3 pages per minute. To calculate the time it will take her to read, we divide 30 pages by 1/3 pages per minute: 30 pages / (1/3 pages per minute) = 90 minutes.
4. Similarly, let's find how long it will take Karen to complete her math homework. Karen has 45 math problems to complete, and her math problem-solving speed is 1/2 problems per minute. To calculate the time it will take her to complete the math problems, we divide 45 problems by 1/2 problems per minute: 45 problems / (1/2 problems per minute) = 90 minutes.
5. Finally, we add the time it takes for Karen to complete her reading homework (90 minutes) and the time it takes to complete her math homework (90 minutes) to find the total time it will take her to do her homework: 90 minutes + 90 minutes = 180 minutes.
Therefore, it will take Karen 180 minutes to complete her homework.
Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of lemon-lime soda to make 12 cups. He pays $3.00 for a 2-liter container of lemon-lime soda and $4.00 for a quart of sorbet. What is the minimum amount he should charge per cup of punch to make a $10 profit? (Remember there are 4 quarts in a gallon.) Your answer should be a dollar amount rounded to the nearest hundredth.(1 point)
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