To determine how long it will take to complete the video game at the current rate, let's set up the equation.
Let \( x \) be the total time (in minutes) it will take to complete the entire game. Since you have completed \( \frac{1}{5} \) of the game in 23 minutes, we can express this relationship with the equation:
\[ \frac{1}{5} x = 23 \]
To solve for \( x \), multiply both sides of the equation by 5:
\[ x = 23 \times 5 \]
Calculating this gives:
\[ x = 115 \]
Therefore, it will take a total of 115 minutes to complete the video game at the current rate.