To solve this problem, we can set up a proportion:
(10 pages / 15 problems) = (30 pages / 45 problems)
To find the amount of time it will take her to do her homework, we need to solve for the missing quantity (time).
Let x represent the amount of time it will take her to complete her homework in minutes.
Therefore, we have:
(10 pages / 15 problems) = (30 pages / 45 problems) = (x minutes / her homework)
We can cross-multiply and solve for x:
10 * 45 = 15 * 30 * x
450 = 450x
Dividing both sides by 450:
x = 1
Therefore, it will take Karen 1 minute to complete her homework.