To determine how many seconds it will take for the diagnostic program to finish, we can set up the problem based on the information provided:
- Current Progress: The program has completed \( \frac{2}{3} \) of its analysis.
- Completion Rate: It takes 1 second to complete \( \frac{1}{6} \) of the analysis.
First, let's find out how much analysis is left:
\[ \text{Remaining analysis} = 1 - \frac{2}{3} = \frac{1}{3} \]
Now we need to determine how much time it takes to complete the remaining \( \frac{1}{3} \) of the analysis based on the given completion rate.
Since 1 second completes \( \frac{1}{6} \) of the analysis, we can find out how long it takes to complete \( \frac{1}{3} \):
- Find out how many \( \frac{1}{6} \) segments are in \( \frac{1}{3} \):
\[ \frac{1}{3} \div \frac{1}{6} = \frac{1}{3} \times \frac{6}{1} = 2 \]
This means that \( \frac{1}{3} \) of the analysis is equivalent to 2 segments of \( \frac{1}{6} \).
- Since it takes 1 second to complete \( \frac{1}{6} \), it would take:
\[ 2 , \text{segments} \times 1 , \text{second/segment} = 2 , \text{seconds} \]
Therefore, the program will finish the remaining analysis in 2 seconds.
Summary
The total time for the program to finish is 2 seconds from the current point.
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