Developer Paul can complete a software data migration project independently in 30 days, whereas Developer Quentin can finish the exact same project in 20 days. Both engineers start working on the project together, but Quentin gets reassigned to another task after 6 days. How many additional days will Paul require to finish the remaining portion of the project on his own?

The correct answer is 15 days.

Step 1: Determine the daily work rates of Paul and Quentin.

Paul can complete the entire project independently in 30 days. His work rate per day is:

$\text{Paul's daily rate}=\frac{1}{30}$

Quentin can complete the exact same project in 20 days. His work rate per day is:

$\text{Quentin's daily rate}=\frac{1}{20}$

Step 2: Calculate the combined work done in one day.

When both engineers work together, their daily work rates add up:

$\text{Combined 1-day work}=\frac{1}{30}+\frac{1}{20}$

To add these fractions, find a common denominator (60):

$\text{Combined 1-day work}=\frac{2+3}{60}=\frac{5}{60}=\frac{1}{12}$

Step 3: Calculate the work completed together in 6 days.

Since both engineers worked together for 6 days before Quentin was reassigned, the portion of the project completed in 6 days is:

$\text{Work done in 6 days}=6\times \frac{1}{12}=\frac{6}{12}=\frac{1}{2}$

Step 4: Determine the remaining portion of the project.

Representing the full project as 1 whole, the remaining fraction of work left is:

$\text{Remaining work}=1-\frac{1}{2}=\frac{1}{2}$

Step 5: Calculate the additional days Paul requires to finish alone.

Paul works alone at a rate of:

$\frac{1}{30}\text{project per day}$

The time needed for Paul to complete the remaining half of the project is:

$\text{Additional days}=\frac{\text{Remaining work}}{\text{Paul's daily rate}}=\frac{1/2}{1/30}=\frac{1}{2}\times 30=15\text{days}$

Therefore, Paul will require 15 additional days to finish the remaining portion of the project on his own.