To find out how long it will take Karen to complete her homework, we need to determine how long it takes her to read 30 pages and complete 45 math problems based on her current rate.
Step 1: Calculate the reading time for 30 pages.
Karen reads 10 pages in 30 minutes. Therefore, the time taken to read 1 page is: \[ \frac{30 \text{ minutes}}{10 \text{ pages}} = 3 \text{ minutes per page} \] To read 30 pages, the time required will be: \[ 30 \text{ pages} \times 3 \text{ minutes per page} = 90 \text{ minutes} \]
Step 2: Calculate the time to complete 45 math problems.
Karen completes 15 math problems in 30 minutes. Therefore, the time taken to complete 1 math problem is: \[ \frac{30 \text{ minutes}}{15 \text{ problems}} = 2 \text{ minutes per problem} \] To complete 45 math problems, the time required will be: \[ 45 \text{ problems} \times 2 \text{ minutes per problem} = 90 \text{ minutes} \]
Step 3: Calculate the total time for both tasks.
Now we sum the time required for reading and for completing math problems: \[ 90 \text{ minutes (reading)} + 90 \text{ minutes (math)} = 180 \text{ minutes} \]
Thus, it will take Karen a total of 180 minutes to complete her homework.