A clock gains 4 minutes after every 4 minutes. You set the correct time in the clock at 6:00 A.M. every day to deal with this issue. What will be the correct time when the time shown by the clock is 8:00 P.M.?

The clock gains 4 minutes every 4 minutes. This means that for every real 4 minutes that pass, the clock shows 8 minutes (4 real minutes + 4 extra minutes).

So, when the clock shows 8:00 P.M., 14 hours have passed on the clock since it was last set at 6:00 A.M.

However, because the clock runs fast, the real time that has passed is less than 14 hours.

To find the real time that has passed, we can set up a proportion. If 8 minutes on the clock is equal to 4 real minutes, then 14 hours (or 840 minutes) on the clock is equal to how many real minutes?

8 clock minutes/4 real minutes = 840 clock minutes/x real minutes

Solving for x gives us x = (4 * 840) / 8 = 420 real minutes

420 minutes is equal to 7 hours.

So, the real time that has passed since 6:00 A.M. is 7 hours, which means the correct time is 1:00 P.M. when the clock shows 8:00 P.M.