it is now between 3 and 4 o'clock and in 20 minutes the minute hand will be as much ahead of the hour hand as it is now behind it. what is the time now?
please help me. Godblesss you
I think its between 3:05 and 3:25 but not sure?
Well, I have a clock here, but it seems to have misplaced its arms. I guess it decided to take some time off. So, unfortunately, I can't help you determine the exact time. But I can tell you this – time flies when you're having fun, so I hope you're enjoying yourself no matter what the clock says!
To solve this problem, we need to understand the relationship between the hour and minute hands on a clock.
First, let's determine the current position of the hour and minute hands. At 3 o'clock, the minute hand points at the 12 on the clock, while the hour hand points at the 3.
Since 20 minutes pass in the given scenario, the minute hand will move by 20 minutes. We also know that the minute hand will be as much ahead of the hour hand as it is now behind it.
In 20 minutes, the minute hand will move 20/60 = 1/3 of an hour.
We can compare the position of the hands before and after the 20 minutes:
Before: The hour hand is at 3, and the minute hand is at 12. The minute hand is 3 positions (hours) ahead of the hour hand.
After: The hour hand will still be at 3, and the minute hand will move 1/3 of an hour ahead. So, the minute hand will be at 12 + 1/3 of the distance between 12 and 1 on the clock.
To calculate this, divide 1/3 by 12 (the total number of hours on a clock) and multiply by 360 degrees (a full circle in degrees).
1/3 * 360 = 120 degrees
So, the minute hand will be at 120 degrees ahead of the hour hand after 20 minutes.
Now, we need to find a time where the hour and minute hands are 120 degrees apart.
On a clock, the minute hand moves 360 degrees every hour, while the hour hand moves 30 degrees every hour.
The difference between their movements is 360 - 30 = 330 degrees every hour.
To find a time where the hands are 120 degrees apart, we can divide 120 by 330:
120 / 330 ≈ 0.3636
This means that for every 0.3636 hours (or approximately every 21 minutes), the hands will be 120 degrees apart.
Since 20 minutes have already passed, we can conclude that the time now is slightly less than 4 o'clock.
Therefore, the current time is between 3 and 4 o'clock, closer to 4 o'clock.
Please note that this calculation is approximate, as the time between 3 and 4 o'clock is not evenly divided into periods where the hands are exactly 120 degrees apart. The answer may vary slightly based on the precise calculation method used.
If after 20 minutes past "now" the minute hand is just as far ahead of the hour as it is behind, the time then clearly must be 3:30
so 20 minutes ago, it must have been 3:10