Agent Y was asked to conduct a detailed interview with a suspect. After 2 hours, the agent had completed 4/9 of the interview. Continuing at this same rate, how long did it take Agent Y to complete the entire interview?

We can solve this problem by setting up an equation. Let's say that x is the total time it takes to do the interview. So far, Agent Y has completed 4/9 of the interview or 4/9x. Since 4/9 of the interview was finished in 2 hours:

4/9x = 2

We can multiply by the reciprocal of 4/9 to get x.

x = 2 * 9/4

x = 4.5

This means that it took Agent Y 4.5 hours to finish the interview.