Let's assume that Luciana's time to complete the job alone is "L" days. Then, Jenna's time to complete the job alone is "L - 14" days (14 days less than Luciana).
The combined work rate of Jenna and Luciana is 1/10 (one house per 10 days), so we can write the following equation:
1/L + 1/(L-14) = 1/10
Multiplying both sides by the least common multiple of the denominators (10L(L-14)), we get:
10(L-14) + 10L = L(L-14)
Expanding and simplifying:
20L - 140 = L^2 - 14L
Bringing all the terms to one side:
L^2 - 34L + 140 = 0
Using the quadratic formula:
L = (34 ± sqrt(34^2 - 41140)) / 2*1
L = (34 ± 12) / 2
L = 23 or 11
Since Luciana can't complete the job in less time than Jenna (L-14 must be greater than 0), we discard the solution L=11. Therefore, Luciana takes 23 days to complete the job alone, and Jenna takes 9 days (L-14) to complete the job alone.
Therefore, it would take Jenna approximately 9 hours to complete the job by herself