Let's denote the time it takes Paola to drywall the basement by herself as "x".
If Rosita takes 32 hours to do the job by herself, then her work rate is 1/32 of the job per hour. Similarly, if Rosita and Paola work together, their combined work rate is 1/18 of the job per hour.
Using the idea of work rates, we can set up the following equation:
(1/32) + (1/x) = (1/18)
To solve for "x", we can begin by multiplying both sides of the equation by the least common multiple of the denominators of the fractions, which is 288:
9 + 288/x = 16
Subtracting 9 from both sides, we get:
288/x = 7
Multiplying both sides by "x", we get:
288 = 7x
Dividing both sides by 7, we get:
x = 41.14
Rounding to the nearest hour, we get that it would take Paola approximately 41 hours to drywall the basement by herself.