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? answer should refer to the amount of time in minutes. pleas explain
We can set up a proportion to solve this problem.
Let "x" be the amount of time it takes Karen to do her homework in minutes.
We know that Karen can read 10 pages and complete 15 math problems in 30 minutes.
So, in "x" minutes, Karen can read (10/x)*30 pages and complete (15/x)*30 math problems.
We also know that Karen has 30 pages to read and 45 math problems to complete.
Setting up the proportion:
(10/x)*30 = 30
(15/x)*30 = 45
To solve for "x", we can cross-multiply:
(10/x)*30 * x = 30 * x
(15/x)*30 * x = 45 * x
Simplifying:
10 * 30 = 30 * x
15 * 30 = 45 * x
300 = 30x
450 = 45x
Dividing both sides of each equation by 30 and 45 respectively:
10 = x
10 = x
So, it will take Karen 10 minutes to do her homework.
are you 100% sure?
Apologies for the confusion in my previous response. Let's reassess the problem.
We know that Karen can read 10 pages and complete 15 math problems in 30 minutes. To find out how long it will take her to do her homework, we can set up a ratio comparing the amount of work she can do in 30 minutes to the total amount of work she needs to complete.
For reading, the ratio is 10 pages / 30 minutes = 1/3 pages per minute.
For math problems, the ratio is 15 problems / 30 minutes = 1/2 problems per minute.
So per minute, Karen can complete 1/3 of a page and 1/2 of a math problem.
If Karen has 30 pages to read, it will take her 30 / (1/3) = 90 minutes to complete the reading.
If Karen has 45 math problems to complete, it will take her 45 / (1/2) = 90 minutes to complete the math problems.
Since she needs to complete both tasks, the total time required would be the higher of the two times - 90 minutes.
Therefore, it will take Karen 90 minutes to complete her homework.