Let's define the variables:

• Let $h$ represent the number of hours Paulina needs to complete her homework.

Paulina has already completed 24 problems out of 42. Therefore, she has $42 - 24 = 18$ problems remaining.

She plans to complete 9 math problems each hour. The total number of problems she can complete in $h$ hours is $9h$.

To find the number of hours $h$ it will take for Paulina to finish her homework, we set up the following equation:

$9h = 18$

This equation represents the situation where the number of remaining problems (18) equals the number of problems Paulina completes in $h$ hours.

Would you like the solution to this equation or any further details?

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Here are some related questions to consider:

1. How many hours would it take if Paulina completed 6 problems each hour instead of 9?
2. What if Paulina had already completed 30 problems? How would that change the equation?
3. How many problems would Paulina complete in 2 hours?
4. What if Paulina wanted to complete her homework in 1.5 hours? How many problems would she need to solve each hour?
5. How many problems would remain if Paulina worked for 1 hour?

Tip: Setting up equations based on word problems helps translate real-life scenarios into mathematical language, making them easier to solve.