At what time...?

Question

At what time, between 3:00 & 4:00 will the sum of the angles of the two hands add up to 270°? The angle of each hand is measured from the 12:00 position, clockwise, to their current time position. Give the exact time. Hour:minute:second (seconds provided with one digit after the decimal point) Provide your solution please.

Answer 1

Let the time taken be x minutes.If the angles are measured from 12:00, then the hour hand has moved 90 deg already.

The minute hand moves at 6 deg/min

The hour hand at 1/2 deg/min,so,

90+x/2+6x=270,so,

90+13x/2=270,so,

13x/2=180,so,

x=360/13,

x=27.692 mins,

x= 27 mins, 41.52 secs,so

the time at which the sum of the angles of the two hands adds up to 270 deg is 3:27:41.5.

Answer 2

let x = amount of time (in minutes) after 3:00 before the blessed event transpires
let 6x = number of degrees that the minute hand sweeps until the blessed event transpires
let x/2 = number of degrees that the hour hand sweeps until the blessed event transpires

What we are looking for is the moment at which the two hands on the clock are arranged such that the sum of the angles (which are counted starting at the 12:00 position) equal 270. Common-sense thinking about this problem tells us that the event will occur after 3:15 (where the sum of angles is just over 180) but before 3:30 (where the sum of angles is just over 270).

270 = (6x) + (90 + x/2)
270 = 90 + (13/2)x
180 = (13/2)x
360 = 13x
27.6923 = x

So, at 3 hr 27.6923 min, the sum of the angles will equal 270. You asked for an hour:minute:second breakdown:

.6923 min = 41.5 seconds

3:27:41.5

Answer 3

At 3:00, the hr hand has moved 90 degrees.

So now we look for the remaining 180 degrees.

In 1 second
the hr hand moves by 1/120 degrees
the minutes hand moves by 1/10 degrees.

Now, let the time taken by them to move a total of 180 degrees be x seconds.

So
x/10 + x/120 = 180
x = 21600/13 = 1661 - 7/13

Now convert it into hrs, minutes and seconds.

Hope this helps.

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Answer 4

The only time this can happen is at 3 o'clock - you have 2 angles between the hands - 90 degrees in one direction and 270 degrees in the other direction.

Answer 5

x+ x /12 + 15 = 45
13/12 x = 30
x = 27.692 minutes = 27 minutes and 41 sec
time is 3:27:41

Answer 6

360/60 = 6 degrees each minuet

3: 28 ...... +/- ..... 60 seconds.

Answer 7

Yeah man..........spot on.