Let's first determine how much of the analysis can be completed in one second.
Given that 1 second completes \( \frac{1}{6} \) of the analysis, we can determine the total time required to complete the entire analysis.
If \( \frac{1}{6} \) of the analysis takes 1 second, then the total time \( T \) required to complete the entire analysis can be calculated as follows:
\[ T = 1 \text{ second} \times 6 = 6 \text{ seconds} \]
So, the entire analysis takes 6 seconds to complete.
Now, if \( \frac{2}{3} \) of the analysis has already been completed, we need to find out how much time has been used and how much time remains.
The portion of the analysis that is left to be completed is:
\[ 1 - \frac{2}{3} = \frac{1}{3} \]
Now, let's calculate how much time is needed to complete \( \frac{1}{3} \) of the analysis.
Since we know it takes 6 seconds to complete the whole analysis, the time required to complete \( \frac{1}{3} \) of the analysis is:
\[ \text{Time for } \frac{1}{3} = T \times \frac{1}{3} = 6 \text{ seconds} \times \frac{1}{3} = 2 \text{ seconds} \]
Thus, the total time for the program to finish the entire analysis after taking into account the \( \frac{2}{3} \) that has already been done is:
\[ \text{Total time} = 2 \text{ seconds} \]
The program will finish the analysis in 2 seconds.
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