To determine how long it will take Karen to complete her homework, we need to calculate the time required for her to read 30 pages and complete 45 math problems based on her current reading and problem-solving speed.
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Reading 30 pages:
- Karen reads 10 pages in 30 minutes.
- Therefore, the time to read 30 pages can be calculated as follows: \[ \text{Time for 30 pages} = \left( \frac{30 \text{ pages}}{10 \text{ pages}} \right) \times 30 \text{ minutes} = 3 \times 30 \text{ minutes} = 90 \text{ minutes} \]
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Completing 45 math problems:
- Karen completes 15 math problems in 30 minutes.
- Therefore, the time to complete 45 math problems can be calculated as: \[ \text{Time for 45 problems} = \left( \frac{45 \text{ problems}}{15 \text{ problems}} \right) \times 30 \text{ minutes} = 3 \times 30 \text{ minutes} = 90 \text{ minutes} \]
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Total Time:
- Now, we add the time it takes to read the pages and complete the math problems: \[ \text{Total Time} = \text{Time for 30 pages} + \text{Time for 45 problems} = 90 \text{ minutes} + 90 \text{ minutes} = 180 \text{ minutes} \]
Thus, it will take Karen a total of 180 minutes to do her homework.
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