At proximately what time after 12oclock will the hour and the minute hand of a clock form angle of 120 degree for tge second time

Question

What is thr answer

Answer 1

Deozdado, since there are 360 degrees in a circle, 120 is 1/3 of that, or four digits apart. The first time they are four digits apart, it's 12:20. The next time is 12:40, because the 8 and 12 are still four digits apart.

Answer 2

When the minute hand makes a full rotation, the hour hand moves 1/12 of a rotation.  120 degrees is 1/3 of 360 degrees, a full rotation.  The first time the difference is 1/3 rotation is when the minute hand is 1/3 of a rotation ahead of the rotation.  The second time will be when the minute hand has 1 rotation - 1/3 more than the hour hand, or 2/3 rotation more than the hour hand.

If the minute hand moves x rotations, then, the minute hand moves x/12 rotations, and their difference changes by x - x/12 = 11x/12.

11x/12 = 2/3

Cross-multiplying, 33x = 24.

x = 24/33 = 8/11

Then, as there are 60 minutes in one rotation, 60 * 8/11 = 480/11 = 43 7/11

The time is 12:43 7/11

 

(Note that the hour hand is at x/12 rotations = 8/11*1/12 = 8/132 = 2/33 rotations, and as there are 12 hours, the hour hand is at 2/33 * 12 = 24/33.

See how this makes sense.  At 12:43 7/11, which is between 2/3 and 3/4 of an hour after 12, the hour hand has moved 24/33, which is greater than 22/33 = 2/3, but less than  24.75/33 = 3/4

 

Answer 3

First you need to figure out the time for the 1st time they form a 120 degree angle. Which can be calculated by 

 

(12/360)(120) or when the minute hand moves to 4 so approximately 12:20. 

 

So the 2 hands must be approximately 4 digits apart to form a 120 degree angle ( it's approximate bc the hour hand isn't exactly on 12 at 12:20). 

 

So now the clock goes back to the hour and it is now 1:00. So to be 4 units away the minute hand is at 5. So the 2nd time occurs at 1:25.